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ACT Math : Solid Geometry

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Example Questions

Example Question #4 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a volume of 512mm^3 ? Round your answer to the nearest hundreth if necessary

Possible Answers:

256mm^2

135.76mm^2

64mm^2

384mm^2

90.51mm^2

Correct answer:

384mm^2

Explanation:

First we need to find the side length of the cube. Do that by taking the cube root of the volume.

$\sqrt[n]{512mm^3}$ = 8mm
Next plug the side length into the formula for the surface area of a cube:

SA = 6*s^2 = 6 *(8mm)^2 = 384mm^2

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

What is the surface area, in square inches, of a cube with sides measuring 4 inches ?

Possible Answers:

64in^2

32in^2

16in^2

96in^2

12in^2

Correct answer:

96in^2

Explanation:

The surface area of a cube is a measure of the total area of the surface of all of the sides of that cube.

Since a cube contains square sides, the surface area is times the area of a square side.

The area of one square side is sidelength sidelength, or 4*4 = 16 in this case. Therefore, the surface area of this cube is 16*6 = 96 square inches.

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

What is the length of the side of a cube whose surface area is equal to its volume?

Possible Answers:

s = 10

s = 6

$s = \sqrt{6}$

There is not enough information to determine the answer.

s = 4

Correct answer:

s = 6

Explanation:

To find the side length of a cube whose surface area is the same as its volume, set the surface area and volume equations of a cube equal to each other, the solve for the side length:

V=s^3: SA=6a^2

Set these two formulas equal to eachother and solve for s.

$\\ s^3 = 6*s^2 \\ \newline \frac{s^3}{s^2}=\frac{6*s^2}{s^2}\\ \newline s = 6$

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

What is the surface area of a cube with a side of length $\textup{3ft}$ ?

Possible Answers:

$9\textup{ ft}^2$

$54\textup{ ft}^2$

$162\textup{ ft}^2$

$27\textup{ ft}^2$

$18\textup{ ft}^2$

Correct answer:

$54\textup{ ft}^2$

Explanation:

To find the surface area of a cube with a given side length, use the formula:
SA = 6s^2 = 6*3^2 = 6*9 = 54

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

Find the surface area of a cube whose side length is .

Possible Answers:

Correct answer:

Explanation:

To find surface area of a cube, simply calculate the area of one side and multiply it by . Thus,

SA=s^2*6=4^2*6=16*6=96

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Example Question #31 : Solid Geometry

Find the surface area of a cube whose side length is .

Possible Answers:

108

Correct answer:

Explanation:

To find surface aarea, simply multiply the area of a face by 6 since there are 6 faces. Thus,

$SA=6\cdot s^2=6\cdot3^2=6\cdot9=54$

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Example Question #32 : Solid Geometry

Find the surface area of a cube with side length .

Possible Answers:

Correct answer:

Explanation:

To solve, simply multiply the face area by . Thus,

SA=s^2*6=1^2*6=6

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

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 #2 : 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 #31 : 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:

1.5x

2.5x

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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ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Find The Surface Area Of A Cube

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

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

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

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

Example Question #31 : Solid Geometry

Example Question #32 : Solid Geometry

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

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

Example Question #31 : Solid Geometry

All ACT Math Resources

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