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SAT Math : Cubes

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Example Questions

Example Question #2131 : Hspt Mathematics

A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m², are needed to fully cover the surface of the cube?

Possible Answers:

100

1000

200

750

500

Correct answer:

750

Explanation:

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m²

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6s^2.)

Each square tile has an area of 5 m².

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m²/5m²= 750

Note: the volume of a cube with side length s is equal to s³. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s³/n³

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Example Question #241 : Geometry

A company wants to build a cubical room around a cone so that the cone's height and diameter are 3 inch less than the dimensions of the cube. If the volume of the cone is 486π ft³, what is the surface area of the cube?

Possible Answers:

513.375 in²

69,984 in²

486 in²

726 in²

73,926 in²

Correct answer:

73,926 in²

Explanation:

To begin, we need to solve for the dimensions of the cone.

The basic form for the volume of a cone is: V = (1/3)πr²h

Using our data, we know that h = 2r because the height of the cone matches its diameter (based on the prompt).

486π = (1/3)πr²* 2r = (2/3)πr³

Multiply both sides by (3/2π): 729 = r³

Take the cube root of both sides: r = 9

Note that this is in feet. The answers are in square inches. Therefore, convert your units to inches: 9 * 12 = 108, then add 3 inches to this: 108 + 3 = 111 inches.

The surface area of the cube is defined by: A = 6 * s², or for our data, A = 6 * 111² = 73,926 in²

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

If the volume of a cube is 216 cubic units, then what is its surface area in square units?

Possible Answers:

108

216

Correct answer:

216

Explanation:

The volume of a cube is given by the formula V = $s^{3}$ , where V is the volume, and s is the length of each side. We can set V to 216 and then solve for s.

$\inline 216 = s^{3}$

In order to find s, we can find the cube root of both sides of the equaton. Finding the cube root of a number is the same as raising that number to the one-third power.

$\sqrt[3]{216}= 216^{1/3}=6=s$

This means the length of the side of the cube is 6. We can use this information to find the surface area of the cube, which is equal to $\inline 6s^{2}$ . The formula for surface area comes from the fact that each face of the cube has an area of $s^2$ , and there are 6 faces in a cube.

surface area = $6s^{2}=6(6^{2})=6(36)=216$

The surface area of the square is 216 square units.

The answer is 216.

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

You have a cube with sides of 4.5 inches. What is the surface area of the cube?

Possible Answers:

$162\hspace{1 mm}in^2$

$121.5\ ft^{2}$

$121.5\hspace{1 mm}in^2$

$10.125\hspace{1 mm}ft^2$

$13.5\hspace{1 mm}ft^2$

Correct answer:

$121.5\hspace{1 mm}in^2$

Explanation:

The area of one side of the cube is:

$4.5\hspace{1 mm}in\times 4.5\hspace{1 mm}in= 20.25\hspace{1 mm}in^2$

A cube has 6 sides, so the total surface area of the cube is

$6\times 20.25 =121.5\hspace{1 mm}in^2$

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Example Question #711 : Sat Mathematics

A cube has a surface area of 24. If we double the height of the cube, what is the volume of the new rectangular box?

Possible Answers:

Correct answer:

Explanation:

We have a cube with a surface area of 24, which means each side has an area of 4. Therefore, the length of each side is 2. If we double the height, the volume becomes $4\cdot 2\cdot 2=16$ .

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Example Question #712 : Sat Mathematics

A cube has a surface area of 10m². If a cube's sides all double in length, what is the new surface area?

Possible Answers:

320m²

40m²

80m²

640m²

20m²

Correct answer:

40m²

Explanation:

The equation for surface area of the original cube is 6s². If the sides all double in length the new equation is 6(2s)² or 6 * 4s². This makes the new surface area 4x that of the old. 4x10 = 40m²

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Example Question #11 : Solid Geometry

What is the surface area of a cube with a side length of 30?

Possible Answers:

1350

9000

900

450

5400

Correct answer:

5400

Explanation:

Write the formula for the surface area of a cube.

A=6s^2

Substitute the side.

A=6(30)^2=6(900)=5400

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

The surface areas of six cubes form an arithmetic sequence. The two smallest cubes have sidelengths 10 and 12, respectively. Give the surface area of the largest cube.

Possible Answers:

8,000

2,400

2,184

1,920

4,640

Correct answer:

1,920

Explanation:

The surface area of a cube can be calculated by squaring the sidelength and multiplying by six. The two smallest cubes therefore have surface areas

$S_{1} = 6 \cdot 10 ^{2} = 600$

and

$S_{2} = 6 \cdot 12 ^{2} = 864$

The surface areas form an arithmetic sequence with these two surface areas as the first two terms, so their common difference is

$d = S_{2} - S_{1} = 864-600 = 264$ .

The surface area of the largest, or sixth-smallest, cube, is

$S_{6} = (6-1)d + S_{1}$

$= 5 \cdot 264 + 600$

= 1,320+ 600

= 1,920

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

Find the surface area of a cube with side length 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the surface area of a cube. Thus,

SA=6s^2=6*2^2=6*4=24

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Example Question #21 : Solid Geometry

Find the surface area of a cube given side length of 3.

Possible Answers:

Correct answer:

Explanation:

To find the surface area of a cube means to find the area around the entire object. In the case of a cube, we will need to find that area of all the sides and the top and bottom. Since a cube has equal side lengths, the area of each side and the area of the top and bottom will all be the same.

Recall that the area for a side of a cube is:

A=s^2

From here there are two approaches one can take.

Approach one:

Add all the areas together.

$SA=A_{side1}+A_{side2}+A_{side3}+A_{side4}+A_{top}+A_{bottom}$

Approach two:

Use the formula for the surface area of a cube,

SA=6s^2

In this particular case we are given the side length is 3.

Thus we can find the surface area to be,

by approach one,

$\\SA=3^2+3^2+3^2+3^2+3^2+3^2 \\SA=9+9+9+9+9+9 \\SA=54$

and by appraoch two,

SA=6s^2=6*3^2=6*9=54 .

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SAT Math : Cubes

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2131 : Hspt Mathematics

Example Question #241 : Geometry

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

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

Example Question #711 : Sat Mathematics

Example Question #712 : Sat Mathematics

Example Question #11 : Solid Geometry

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

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

Example Question #21 : Solid Geometry

All SAT Math Resources

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