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G-MG [686730]

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Class

Date

Read the following and answer the questions below:

College Apartments

College Apartments

The number of students enrolled in a local college is increasing rapidly, andthere is limited space in the high-rise residence halls on the college campus.Because of this, more students are moving to apartments near campus. Thecollege is working with a real estate development company to plan two newapartment complexes to provide housing for the additional students.

The college has requested that each apartment complex have housing for atleast 3 students, as well as such amenities as laundry and common studyareas, so that it provides a similar environment to that of the residencehalls. !ach of the residence halls on campus is "" stories tall# " floors eachcontain 3$ one-bedroom dormitories, and " floor contains a study lounge,cafeteria, social area, and laundry room.

%s shown in the map of the area near the college campus below, one newapartment complex will be to the west of campus and one will be to theeast. The new developments are titled &ampus 'est %partments and&ampus !ast %partments, respectively.

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(ichael and )ancy work for the development company, and they are eachmanaging the teams that are designing these two apartment complexes.They both want to create apartments that meet the college*s requirementsand that students want to live in.

(ichael*s team is developing a plan for an apartment complex wherestudents will live in $ large three-story apartment buildings. +ne buildingwill have $ two-bedroom apartments on each floor, and the other buildingwill have " four-bedroom apartments on each floor. There will also be aseparate, smaller building that contains the management office, a common

area with a food court, a study center, and a laundry facility. (ichael is alsoplanning to put picnic tables outside so students can have an additional areain which to socialie, and students will have the option of getting a parkingspace in the apartment complex*s parking lot.

nstead of a few large apartment buildings, )ancy*s team has decided thatmany smaller apartment buildings will make the apartment complex feel

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more welcoming. This development will be made up of "/ four-storyapartments that each have $ three-bedroom apartments on each floor.0aundry will be included in each apartment. n this complex, there will alsobe two smaller buildings that serve as common areas. These buildings willinclude computer labs, pool tables, and a mini-market. There will not be a

parking lot, but there will be an outdoor basketball court and a sandvolleyball court.

1tudents on campus are eager to secure apartments and roommates fornext year and are comparing their options to determine which developmentis best for their needs.

1.2ead &ollege %partments4 and answer the question.

(ichael and )ancy are creating mathematical models to illustrate howmany students each type of apartment building or dorm can house oneach of its floors. They assume that each student will have his or herown bedroom. 'hich model is the best comparison5

A.

B.

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C.

D.


The Lionfsh Threat

The Lionfsh Threat

6ishermen and environmentalists are concerned about the spread of aninvasive species known as the lionfish. +riginally found in the 7acific and

ndian +ceans, this ornamental fish has been highly popular with aquariumowners. t is believed that one such enthusiast may have released severalspecimens into the waters off the %tlantic coast of 6lorida or the &arolinas.The impact has had significant consequences on the local reef system.

0ionfish prey upon commercially important species such as snapper andlobster. n some areas, the introduction of lionfish has reduced those

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populations to one-tenth of their former sie. 0ionfish also compete againstother predators such as the coney grouper. They are able to consume preyspecies at two-and-a-half times the rate of their competitors. t is for thisreason that lionfish may be contributing to a decline in the number ofconeys as available food sources become harder to find.

(arine biologists are concerned about the long-term effects of lionfishpredation along the %tlantic &oast. To monitor the extent of increase inlionfish numbers, they set up a series of survey sites off the coast of )orth&arolina. They have been able to count the number of fish observed at eachsite and calculate the average. This makes it possible to compare the annualpopulation density of lionfish per acre. The bar graph below shows the datacollected annually from the survey sites.

2.2ead the passage The 0ionfish Threat4 and then answer the questions.

Part A

+n average, approximately how many more lionfish were there per acrein $8 than in $95

Part B

%pproximately how many times greater was the lionfish population per

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acre in $8 than in $:5

Part C

f xrepresents the total number of lionfish observed in $:, write anexpression, in terms of x, that represents the number of acres of

habitat in $:.

Part D

f " square mile ; : acres, what was the approximate lionfishpopulation density per square mile in $85

Part E

f the lionfish density per acre in $" was half the density in $8, oneof the causes might be a decrease in lionfish population. 'hat mightanother cause be5

Part F


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Designing a Hotel

Designing a Hotel

=asmin is a high school student who wants to be an architect. % localarchitecture design firm is sponsoring a contest to design a new high-rise

hotel building that will be located in the downtown area of the city in which=asmin lives. The winner of the contest will earn an internship with thearchitecture firm, and =asmin has decided to submit a design. 1he hopesthat she will be able to learn more about architecture by creating the designand learn even more if she wins the internship.

=asmin wants hotel guests to be able to see the city and en>oy the warmweather, so one of the first elements she puts in her design plan is a rooftopdeck. 1he asks her friends at school what they like to do when they visit ahotel, and the most common response is to go swimming. =asmin decidesto combine the two ideas and put the hotel pool on the roof.

1he also incorporates a caf? area so that people can eat while en>oying theview. Then, she adds an area between the caf? and the pool where peoplecan sit at tables in sun chairs, admiring the city skyline.

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%nother thing =asmin wants is for her building to stand out among the othertall buildings downtown. 1he uses nonvertical supports to create aninteresting pattern on the front of the building. The main structural supportswill be inside and will not be visible from the outside.

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0astly, =asmin plans to cover most of the outside of the building with darkglass. This way, she thinks, the building will look shiny and modern, and allof the hotel*s guests will be able to have a great view of the city from their

rooms.=asmin submits her design plans to the contest before the deadline andwaits anxiously to find out whether she has won. 1he knows that winningthis contest could be the start of the career she*s hoping for.

3. 2ead @Aesigning a


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A. #(

B. "#2

C. )#"

D. )#)

5. Pet Fence

Aana is planning to build an enclosure in her yard so that her dogs canplay in a secure area. 1he is planning to use fencing that comes in rigid-foot-long sections. 1he cannot bend the individual sections, but shecan >oin them at any angle to form different polygons. Aana has enoughmoney to buy $: sections of fencing, including one with a gate. Aanaplans to use all $: sections of fencing when building the enclosure forher dogs.

7art %. Aana first considers making a rectangular enclosure. n the table

below, list all possible ways Aana could use the fencing to make anenclosure that has an area of at least 8 square feet. 'hat is thegreatest rectangular area Aana could enclose with the $: sections offencing5 !xplain your answer.

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7art B. Aana decides to sketch models of the rectangular enclosures.1he uses tick-marks to show each section of fencing on the models, andshe labels what will be the actual length and width of the enclosures. f

represents two pieces of fencing placed next to each other, use aruler or graph paper to sketch models of all of the possible enclosuresthat have an area of at least ", square feet. 0abel the models withwhat will be the actual lengths and widths of the enclosures.


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regular octagon with tick-marks to show how many fence sections wouldbe needed for each side. nclude the length of each side, in feet. Then,divide the octagon into sections so that you can compute its area insquare feet, and sketch your divisions on your model. 1how your workand label the lengths you used in your calculations. 'hen appropriate,

leave side lengths in radical form. 6or your final answer, round the areato the nearest square foot.

7art !. f Aana uses all $: pieces of fencing as the sides of the enclosure,how could Aana construct the enclosure in order to maximie the area5Aescribe the configuration and explain your answer.

6.Brianna made a rame# 3he connected the opposite corners o the rame with wire'as shown in the diagram 4elow#

Brianna wants to ma5e sure that the interior angles on the rame are right angles#

-hich method could Brianna use to .eri/ that areall right angles1

A.6easure and to ma5e sure the/ are e0ual' measure and to ma5e surethe/ are e0ual' and measure and to ma5e sure the/ are e0ual#

B.6easure and to ma5e sure the/ are e0ual' measure and to ma5e sure

the/ are e0ual' and measure and to ma5e sure the/ are e0ual#

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C.6easure and to ma5e sure the/ are e0ual' and measure and to ma5e

sure the/ are e0ual#

D.6easure and to ma5e sure the/ are e0ual' and measure and to ma5e

sure the/ are e0ual#

7.The ta4le 4elow lists the population and area o our di7erent states rom the same/ear#

Population and Area

3tate Population

Area

8s0uare miles9

Alas5a *,*':2, "(!'2(

Georgia )'+)*'"2 "(':+:

;ansas ,'*))'+) )+'),2

Te


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thic5ness o his gold 4ar1

A. !#2 cm

B. !#: cm

C. 2#2 cm

D. *#" cm

9.Gerald has a punch 4owl in the shape o a hemisphere as shown 4elow#

>ne cup is e0ui.alent to appro


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10

.

The density of water is " kilograms per cubic meter, and the densityof ice is about 8" kilograms per cubic meter. f /C/ kilograms of waterand $C/ kilograms of ice is combined in a container, about how much

volume would the mixture take up5

A.

B.

C.

D.

11

.

Charles 4ought a fsh tan5 in the shape o a prism with a 4ase shaped li5e a regularhe


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A. +)#( gallons

B. )#* gallons

C. "*#+ gallons

D. :(#, gallons

12.The fgure 4elow shows a compost 4in#

-hich process is most li5el/ to 4e used to estimate the total surace area o thecompost 4in1

A. computing the area o * rectangles

B. computing the area o trape?oids and , rectangles

C. fnding the perimeter o the 4ase and multipl/ing 4/ the height

D.fnding the mean o the perimeters o the 4ase and the top and multipl/ing 4/

the height

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13

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Datie is using graph paper to sketch a design for a flat wooden benchthat will have a rectangular seat. The front and side views that Datiesketched are shown below.

f Datie uses a scale on the graph paper in which each box representsa -inch by -inch square, what are the dimensions of the seat of thebench Datie is designing5

A. $ feet long by $./ feet deep

B. / feet long by $ feet deep

C. /./ feet long by $./ feet deep

D. " feet long by / feet deep

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6r# 3mith 4uilt a rectangular@shaped sand4o< or his children' measuring eet 4/ eet 4/ * inches# 3and has a densit/ o appro


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A. "*

B. :)

C. ,,

D. *(,

15

.

Eulius is in charge of planting a peach orchard that covers "/ acres.


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%ndone

sia(+'!::#*, ,2'+)+'!!

atar '+"#)" +'*:*'"*2

Thailand

+:)'"*#2 *2'","'!*,

-hich countr/ is most densel/ populated1

A. atar

B. France

C. Thailand

D. %ndonesia

17

.

Build a &orner &upboard

=ou are taking an interest in carpentry and want to design a cornercupboard for books and knickknacks. % corner cupboard, or cabinet, isshaped like a triangular prism and fits into the corner of a room. =ou usegeometric methods to work out the specifications for the cabinet.

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7art %. Fiven the space you have available, you are thinking that thecabinet should come out "9 inches Gin.H from the corner along each wall.


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each book at the edge of the shelf, what is the maximum number ofbooks you can put in the row5 Araw a sketch, show your work, andexplain your answer.

7art 6. =ou are thinking about making a small 3-in. rail for the top shelf,

as shown in darker gray below.

1how how you could cut a piece of wood like the one below to make the

rail with the least waste possible. 0abel lengths and angles. 'hat is theminimum length of wood that you would need5

18

.

The wall of a kitchen has a length of "$ feet GftH and a height of " ft.

The wall is to be tiled to cover half of its height and its entire length.


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The c/lindrical tan5 inside a water heater has a ,!@inch diameter and a "(@inch height#

$>ne British thermal unit is needed to raise the temperature o + pound o water

+F when under + atmosphere o pressure#

$ >ne cu4ic oot o water weighs appro4ect -eight 8pounds9 olume 8gallons9

A 2"# #

B *2#) (#"

C +!#, +,#*

D ,2:# 2+#!

The densit/ o water is appro


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A. >4ect A

B. >4ect B

C. >4ect C

D. >4ect D

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Platinum has a densit/ o ,+#" grams per cu4ic centimeters# % a ring made o pureplatinum has a mass o *#2 grams' what is its appro


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D. ,((,

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% gas at standard temperature and pressure was measured as having amass of ":9/ grams GgH in a volume of C/ liters G0H. 'hich of thefollowing gases could it be5

A. carbon dioxide

B. carbon monoxide

C. helium

D. oxygen

24

.

The owner o an ice cream store wants to ma5e a wae cone that has the same.olume as 2 scoops o ice cream#

$ Each scoop o ice cream is in the shape o a sphere#

$ The wae cone will 4e in the shape o a cone with a diameter that is +#("times the diameter o a scoop o ice cream#

Based on this inormation' which statement is true a4out the height o the waecone1

A.The height o the cone should 4e a4out 2# times the radius o the sphere#

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B.The height o the cone should 4e a4out 2#: times the radius o the sphere#

C.The height o the cone should 4e a4out *#: times the radius o the sphere#

D.The height o the cone should 4e a4out (#+ times the radius o the sphere#

25

.

1ophie needs to determine the amount of water that will fit into her newvase, shown below.

'hich combination of geometric shapes can she use to bestestimatethe vase*s volume5

A. % cone and a hemisphere

B. % cylinder and a sphere

C. % truncated cone and a sphere

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D. % truncated pyramid and a hemisphere

26.

The top .iew o a des5 is shown 4elow' where and

atalie wants to construct this des5# -hich o the ollowing could not 4e the shapesused to construct the des5 top1

A. + pentagon and , congruent rectangles

B. + rectangle and , congruent pentagons

C. + rectangle and , congruent trape?oids

D. + trape?oid and , congruent 0uadrilaterals

27.Two steps in constructing a tangent line rom Point Pto Circle Oare shown#

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-hich method will result in fnding a point o tangenc/ in the neect is made of two geometric figures. 'hich ob>ect canbe bestmodeled by a cylinder and a cone5

A. a human torso

B. an ice cream cone

C. a camera with lens

D. a sharpened pencil

29The population densit/ o %celand in ,!+, was 2#!: persons per s0uare 5ilometer# %%celand has an area o +!2'!!! s0uare 5ilometers' how much would the population

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. need to increase so that the densit/ increases to 2#," persons per s0uare5ilometer1

A. +!',*!

B. +*')!

C. ,'(,!

D. 2+'*:,

30

.

The densit/ o pure water at C is + g=cm2# Three o the su4stances in the chartwill oat in water# 3u4stances with densities less than that o water will oat inwater#

6ass and olume o

Four 3u4stances

3u4stance 6ass olume

A +#: 5g ,#! m2

B ,#( g 2#! cm2

C +!!! 5g ,!! m2

D !#+): g !#+,* cm2

-hich su4stance will not oat in water1

A. 3u4stance A

B. 3u4stance B

C. 3u4stance C

D. 3u4stance D

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31

.

The ta4le shows the air conditioning s0uare ootage range or a house located inthe northern part o the Inited 3tates# A one@oor rectangular@shaped house is

appro


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The pipes can 4e installed either along 6ain 3treet or in Cit/ Par5 along and #The council will use the inormation in the ta4le 4elow to determine the leasten the map' uadrilateral FGHKis a rectangle with GH HJ JK KF !! eet#Based on this inormation' which decision will result in the least e


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% the .egeta4le garden is to ha.e an o.erall densit/ o " plants per s0uare oot'which .egeta4le should 4e planted in the empt/ s0uare oot1

A. Corn

B. Beans

C. >nions

D. Eggplant

34

.

1andy is designing cartons to hold cans of beans. The cartons are in theshape of a rectangular prism, and the cans are cylinders measuring.9/9 centimeters GcmH in diameter and "." cm tall. The carton mustbe able to hold 3 cans on one layer and have a length no greater than

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/ cm.

Aue to restrictions on the machine that creates the cartons, 1andy firstcompletes her calculations and then rounds her results up to the next.$/ cm.

7art %Aetermine the dimensions for the base of the carton that would bestaccommodate 3 cans with the least amount of space left over. 1howand explain your work.

7art Bsing the dimensions found for part %, determine the amount of area)+T covered by the cans on the base level. 1how your work. 2ound youranswer to the nearest hundredth.

7art &The material for the cans weighs .// ounces per square centimeter.


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A. ;ing

B. Benton

C. 3po5ane

D. -hatcom

36

.

A container o uice is in the shape o a c/linder with a height o +, centimeters# %the container holds 2"" cu4ic centimeters o uice' which is closest to the diametero the container1

A. 2#!( centimeters

B. "# centimeters

C. *#+ centimeters

D. +!#)) centimeters

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.

T%1DI 1how work for all parts using information from the table below,when needed.

Florida 6innesota ermont -isconsin

0and %rea Gsq. mi.H /3,:C: C8," 8,$"C

7opulation "8,3"9, $, /,C$,

7opulation Aensity C. "/.CPart AI 7opulation density is the number of people living in a state, persquare mile. &omplete the table above. 2ound populations to thenearest thousand.

Part BM 'hich pair of states in the table has the most similar land areas5!xplain why their population densities differ.

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Part CI 1uppose that /, people move from 'isconsin to (innesotaover the next five years. !xplain by how much 'isconsin*s populationdensity would decrease and (innesota*s would rise. Then, explain whythe population density in one state changes more than in the other.

Part DI


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-hich sum o measures would 4e 4est to estimate the ma


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B.

C.

D.

41

.


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. a diameter of $ ft. 'hich statement about the trunk of Diana*s tree istrue5

A.t can be modeled using a cone with a volume of cubic feet.

B.t can be modeled using a cone with a volume of cubic feet.

C.t can be modeled using a cylinder with a volume of cubic feet.

D.t can be modeled using a cylinder with a volume of cubic feet.

4

3.

6rom 1tone Tablets to %tomic Tablets

se the concept of density to quantify the amount of information thatcan be stored on different types of media, such as &As, AJAs, andcomputer hard drives. Aata density is often expressed as the amount ofinformation per unit of area of the storage system.

Aata are stored using the binary Gbase-$H system, which representsnumbers and other symbols using only the digits and ". The smallestpiece of information is a bit, which is a single digit, either or ". +nebyte is equal to 9 bits. =ou will use this information and the followingequivalencies to answer the questions in this task.

%n ancient stone carving could hold a few bits of information per squareinch. &ompare that to the storage density of modern media.

7art ". % &A-2+( can store about / megabytes of data on one side

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Grepresented by the darker gray outer circle in the diagram belowH. % &Ais about :.C inches in diameter. The radius of the inner track of the &A is.8 inch. Aescribe how to calculate the storage density of the &A inmegabytes per square inch. =ou should show how to set up theequations using the given numbers, but you do not need to solve them.

7art $. There are approximately .:/ square centimeters in " squareinch. !xplain how to calculate the storage density of the &A inmegabytes per square centimeter if you know the density in megabytesper square inch.

7art 3. % AJA optical disk has the same recording area as a &A-2+( but

can store about C gigabytes. 6ind the storage density in megabytes persquare centimeter. se the approximate numbers of bytes given aboveand round the area to the nearest square centimeter. Then write ageneral statement comparing the storage density of a &A with that of aAJA.

7art :. )ew research into storing data on atoms has opened thepossibility of desktop computers with : terabytes of memory. f one ofthese new computers had the same amount of storage area as an oldcomputer with : kilobytes of memory, about how many times greaterwould the data density be5 se the approximate numbers given above.

44

.

EricaNs amil/ has a concrete patio outside the home# The densit/ o the concrete is

appro


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mass o the concrete in this patio1

A. (#:: 5g

B. 2+(#* 5g

C. +,'*!! 5g

D. "!!'!: 5g

45.-hich measure would 4e 4est to estimate the amount o a4ric necessar/ to ma5ean um4rella1

A. .olume o a sphere

B. surace area o a sphere

C. .olume o a hemisphere

D. surace area o a hemisphere

46

.

The densit/ o gold is +:#2 grams per cu4ic centimeter# A weight o + ounce ise0ui.alent to a mass o a4out ,)#2" grams# -hich o these is closest to the sidelength o a cu4e@shaped 4loc5 o gold that has a weight o ) ounces1

A. ,#,( centimeters

B. 2#2 centimeters

C. :#!: centimeters

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D. ++#(" centimeters

47.

-hich feld has a densit/ o appro


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B.

C.

D.

49

.

Compan/ A sells chocolate candies with a s0uare 4ase o side length , centimeters

and a height o centimeter# Compan/ B sells chocolate discs with a radius o

+ centimeter and a height o centimeter# Both companies pac5age their chocolatesin identical tin containers that each hold one la/er o ,) chocolates# ulio 4u/s a tino chocolates rom Compan/ A' and Carmen 4u/s a tin o chocolates romCompan/ B# -hich conclusion can 4e supported 4ased on the inormationpro.ided1

A. Carmen and ulio purchased a4out the same .olume o chocolate#

B. ulio purchased a4out more chocolate than Carmen#

C. Carmen purchased a4out more chocolate than ulio#

D. ulio purchased a4out more chocolate than Carmen#

50

.

A cu4e@shaped pac5ing 4o< li5e the one shown 4elow is used to pac5 a stac5 odinner plates#

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% the .olume o the 4o< is +'!!! cu4ic inches' what is the ma


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52

.

A mi


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-hat is the area o the circle o the e/e1

A.

B.

C.

D.

55

.

During cold months' when the di7erence 4etween the inside temperature andoutside temperature is 2!F' it ta5es a4out 2#: British thermal units 8BTI9 per cu4icoot to heat a room# -hich o the ollowing is closest to the num4er o Britishthermal units needed to heat a room with a ,!@oot 4/ +*@oot rectangular oor andan )@oot ceiling1

A. +)':), BTI

B. ::) BTI

C. +,) BTI

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D. *"* BTI

56.

Brian purchased a rectangular@shaped granite countertop or the island in his

5itchen# The granite sla4 measures (, inches 4/ , inches 4/ +#," inches# % thedensit/ o granite is +(! pounds per cu4ic oot' how much does the countertopweigh in pounds1

A. +"(#"

B. ,:(#"

C. 2(+#:

D. ,"#!

57

.

The spacing o plants in a .egeta4le garden is important so that plants can growproperl/# The diagram 4elow shows a .egeta4le garden that measures 2 eet 4/ 2eet#

-hat is the appro


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A. "#

B. )#,

C. +*#2

D. :#!

58

.

The population o the Inited 3tates in two di7erent /ears is shown in the ta4le4elow#

The total land area o the Inited 3tates is 2'"+'( s0uare miles# Based on thisinormation' which is closest to the o.erall change in population densit/' in peopleper s0uare mile' or the Inited 3tates 4etween ,!!! and ,!+!1

A. !#+2 people per s0uare mile

B. !#(( people per s0uare mile

C. (#(, people per s0uare mile

D. +*#*( people per s0uare mile

59

.

'hich combination of three-dimensional shapes could be used to bestmodel the table shown below5

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A. rectangular prisms and " cube

B. : right triangular prisms and " cube

C. $ rectangular prisms and $ right triangular prisms

D. 3 right triangular prisms and $ rectangular prisms

60

.

Martins Swimming Pool

(artin is planning to construct a swimming pool behind his house. Thearchitect shows him a plan for the swimming pool. The pool, if viewedfrom the top looks like a : ft long and $ ft wide rectangle. The pool is

divided into two equal sections along its lengthLthe shallow section andthe deep section. The shallow section has a constant depth of / ft. +ncethe shallow section ends, the floor of the pool starts sloping until itreaches a maximumdepth of $ ft at the other end of the pool.

7art %. 'hat is the length of the slope of the deep section of the pool5Araw a two-dimensional side view of the swimming pool to show theshallow and deep sections. 2emember to write the measures of all sides.

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7art B. (artin contracts a construction company to dig up earth for theswimming pool. The company charges M"/ per hour and estimates thatit will be able to complete the >ob within 9 hours.


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B. a cylinder

C. a triangular prism

D. a rectangular prism

62

.

% population density map of a county is given below. +ne square unitrepresents one square kilometer.

7art %.


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The county gives out grants for housing developments. 'hich areashould be the top priority for the county officials to encourage thebuilding of additional housing units5 !xplain. &reate a table to show howmany units they should build in each area. Be sure to take the range of

population into account and support your answer with numbers obtainedfrom the information above.

se words, numbers, andNor pictures to show your work.

63

.

3arah has , spherical 4alls with radii o * mm# >ne 4all is pure gold and theother is pure sil.er# % the densit/ o gold is +:#2 g=cm2and the densit/ o sil.er is

+!#" g=cm2' a4out how much greater is the gold 4allNs mass than the sil.er 4allNsmass1

A. ) grams

B. : grams

C. )!!! grams

D. !!! grams

64 A cand/ compan/ sells ta7/ in our containers shaped li5e right prisms# The ta4le4elow shows the shapes o the 4ases and dimensions o each container#

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.

-hich container has the least ratio o surace area to .olume1

A. Container +

B. Container ,

C. Container 2

D. Container

65

.

%n +:::' the I#3# territor/ o Guam had an appro


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D. "!!

66.

The ta4le shows the num4er o .egeta4le plants and the num4er o planted acres

or armers#

um4er o Plants in Planted Acres

T/pe o Plants um4er o Plants Planted Acres

Farmer A Corn +#2* O +!* )!

Farmer B 3o/4ean Plants +#" O +!( +"!

Farmer C Green Beans "#, O +!* "!

Farmer D Pepper Plants "#) O +!" ,!

-hich armer has the most densel/ planted feld1

A. Farmer A

B. Farmer B

C. Farmer C

D. Farmer D

67

.

%n +:::' the countr/ o 6onaco had a population o appro


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C. 2'!!!

D. 2'!!!

68

.

A container shaped li5e a rectangular prism holds #! 5ilograms o anun5nown gas# The dimensions o the container are , meters 4/ , meters 4/!#" meter#

Densit/ o Gases

Gas Densit/ 8g=cm29

Helium !#!!!+()

H/drogen !#!!!!:

Car4on Dio


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B.

C.

D.

70

.

(r. !vans built the model below to show the dimensions of the new barnhe is planning to build on his farm.

7art %. 'hat 3-dimensional shapes did (r. !vans use to build his modelof the barn5

7art B.


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next to his barn, as show by the diagram below.

'hich geometric solids bestrepresent the shape of the silo5 f the baseshape of the silo is 9 ft taller than the barn and has a diameter of $ ft,

how much grain will his silo hold, to the nearest cubic foot5

se words, numbers, andNor pictures to show your work.

71

.

%n ,!+,' an estimated )+'("('*!! people li.ed in German/# 3ince German/Ns areais 2"('!,+ s0uare 5ilometers' which is closest to German/Ns population densit/ per

s0uare 5ilometer in ,!+,1

A. +((

B. ,,:

C. ,(*

D. 2(

72

.

% standard soccer ball is shown below. The soccer ball is a model of apolyhedron where every vertex connects a regular pentagon and tworegular hexagons.

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The deficitof a vertex of a polyhedron is defined to be 3 minus thesum of the degrees of the angles that meet at the vertex. 6or a convexpolyhedron, the total deficit of all vertices always adds up to C$.


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-hat is the o.erall densit/' in residents per s0uare /ard' or the entire apartment4uilding1

A. !#!+2 people per s0uare /ard

B. !#!," people per s0uare /ard

C. !#!,) people per s0uare /ard

D. !#!2" people per s0uare /ard

74

.

% certain town has an area of 3 square kilometers and a population of"39 people. f a box represents one square kilometer and each dotrepresents one person, which model is the B!1T representation of thepopulation density of this town5

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A.

B.

C.

D.

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75

.

%s part of a home-improvement pro>ect, %ndy painted " walls in

his house. The area of each wall is The paint he bought comes in$ gallon cans.

%bout how many cans did %ndy need if " gallon of paint covers

A. /

B. "

C. ""

D. $$

76

.

Crista has a 4ag o +! mar4les' where each mar4le has a diameter o inch# The

mar4les are made o agate' which has a densit/ o +#" ounces per cu4ic inch# otincluding the weight o the 4ag' a4out how much do the +! mar4les weigh inounces1 8Ise Q R 2#+9

A. !#,

B. +#:

C. :#

D. +"#2

77 Am/ drew a design consisting o +" congruent circles surrounded 4/ an e0uilateral

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. triangle as shown 4elow#

The sides o the triangle are tangent to each o the +, outer circles# Each circle istangent to e.er/ adacent circle# -hich e


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% carpeting costs "#! per s0uare oot' what is the total cost o the new carpetingor this room1

A. ,"*#"!

B.,),#+"

C. +',),#"!

D. +'""+#)2

79

.

Jeronica*s science class is studying density, and each student is asked to

bring in an ob>ect to determine its density. Jeronica brings in a brickthat weighs two pounds and is inches long, 3 inches wide, and $inches tall.


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A.The brick has a greater volume than the block and a smaller mass,so the brick is less dense than the block.

B.The block has a smaller volume than the brick and a greater mass,so the brick is more dense than the block.

C.The brick is half the volume of the block but more than half themass, so the brick is more dense than the block.

D.The block is twice the volume of the brick and more than double themass, so the brick is less dense than the block.

80.The fgure 4elow shows the components o a c/lindrical well#

-hich measurement is most li5el/ to 4e used to determine the diameter o thewell cap1

A. the capacit/ o the c/lindrical well casing

B. the circumerence o the c/lindrical well casing

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C. the depth o the c/lindrical well casing 4elow the ground

D. the height o the c/lindrical well casing a4o.e the ground

81

.

% block of wood is $ feet inches long, inches wide, and 3 inches tall.

t weighs pounds. To the nearest pound, what is its density inpounds per cubic foot5

A. /3

B. /"

C. 3/

D. 33

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