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ACT Math : Geometry

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Example Questions

Example Question #22 : Cubes

What is the sum of the number of vertices, edges, and faces of a cube?

Possible Answers:

None of the answers are correct

Correct answer:

Explanation:

Vertices = three planes coming together at a point = 8

Edges = two planes coming together to form a line = 12

Faces = one plane as the surface of the solid = 6

Vertices + Edges + Faces = 8 + 12 + 6 = 26

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Example Question #11 : How To Find The Volume Of A Cube

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

Possible Answers:

6.73x³

5.28x³

4.18x³

8.00x³

3.82x³

Correct answer:

3.82x³

Explanation:

V_cube = s³ = (2x)³ = 8x³

V_sphere = 4/3 πr³ = 4/3•3.14•x³ = 4.18x³

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Example Question #61 : Solid Geometry

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Possible Answers:

2.5x

1.5x

Correct answer:

Explanation:

Weight = Density * Volume

Volume of Gold Cube = side³= x³

Weight of Gold = 16 g/cm³* x³

Weight of Glass = 3/cm³ * side³

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x³ = 2 * side³

side³ = 16/2* x³= 8 x³

Take the cube root of both sides:

side = 2x

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Example Question #4 : How To Find The Volume Of A Figure

Chemicals to clean a swimming pool cost $0.24 per cubic foot of water. If a pool is 6 feet deep, 14 feet long and 8 feet wide, how much does it cost to clean the pool? Round to the nearest dollar.

Possible Answers:

$\$150$

$\$672$

$\$202$

$\$161$

$\$184$

Correct answer:

$\$161$

Explanation:

The volume of the pool can be determined by multiplying the length, width, and height together.

$V = 6 \times 8 \times 14 = 672 ft^{3}$

Each cubit foot costs 24 cents, so:

$672ft^3\times \$0.24=\$161.28\approx \$161$

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Example Question #62 : Solid Geometry

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Possible Answers:

Correct answer:

Explanation:

If we let represent the length of an edge on the smaller cube, its volume is $x^{3}$ .

The larger cube has edges three times as long, so the length can be represented as . The volume is $(3x)^{3}$ , which is $27x^{3}$ .

The large cube's volume of $27x^{3}$ is 27 times as large as the small cube's volume of $x^{3}$ .

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Example Question #63 : Solid Geometry

A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

Possible Answers:

16 in^3

8 in^3

150 in^3

134 in^3

160 in^3

Correct answer:

134 in^3

Explanation:

$Volume_{Tank} = Width \cdot Depth \cdot Height$

$Volume_{Tank} = 3in \cdot 5in \cdot 10in = 150 in^3$

$Volume_{Cube} = (Side)^3 = (2in)^3 = 8 in^3$

$Volume_{Water}=Volume_{Tank}-2(Volume_{Cube})$

$Volume_{Water}=150-2(8)$

$Voume_{Water}=150-16$

$Volume_{Water}=134in^3$

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Example Question #3 : How To Find The Volume Of A Cube

What is the volume of a cube that has a side length of inches?

Possible Answers:

63in^3

343in^2

21in^3

49in^2

343 in^3

Correct answer:

343 in^3

Explanation:

We are given the side length of a cube so we simply plug that into the formula for the volume of a cube.

That formula is V =s^3 , and so the correct answer is

V=7^3=343in^3 .

Make sure to check your units, 343in^2 is the correct number, but the units are squared rather than cubed.

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Example Question #1 : How To Find The Volume Of A Cube

What is the volume of a cube with a side of length 1 cm?

Possible Answers:

0cm^3

6cm^3

3cm^3

1cm

1cm^3

Correct answer:

1cm^3

Explanation:

The formula for the volume of a cube with a side of length is:
$\\V = s^3 \\V= 1^3 \\V= 1cm^3$

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Example Question #8 : How To Find The Volume Of A Cube

A cube of sponge has volume 1000 cm^3 . When water is added, the sponge triples in length along each dimension. What is the new volume of the cube, in cubic centimeters?

Possible Answers:

2700cm^3

9000cm^3

30000cm^3

27000 cm^3

3000cm^3

Correct answer:

27000 cm^3

Explanation:

If our original cube has a volume of 1000cm^3 , then the length of one of its edges is $\sqrt[3]{1000} = 10cm$ . Triple each edge to 30cm , then cube the result, and we obtain 30^3 = 27000cm^3

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Example Question #2 : How To Find The Volume Of A Cube

Find the volume of a cube with side length 10.

Possible Answers:

100

1000

$10\sqrt{2}$

600

Correct answer:

1000

Explanation:

To find volume, simply cube the side length. Thus,

V=s^3=10^3=1000

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ACT Math : Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #22 : Cubes

Example Question #11 : How To Find The Volume Of A Cube

Example Question #61 : Solid Geometry

Example Question #4 : How To Find The Volume Of A Figure

Example Question #62 : Solid Geometry

Example Question #63 : Solid Geometry

Example Question #3 : How To Find The Volume Of A Cube

Example Question #1 : How To Find The Volume Of A Cube

Example Question #8 : How To Find The Volume Of A Cube

Example Question #2 : How To Find The Volume Of A Cube

All ACT Math Resources

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