Solid Geometry

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ACT Math › Solid Geometry

Questions 1 - 10
1

Find the surface area of a cube with side length .

Explanation

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

2

If the surface area of a cube equals 96, what is the length of one side of the cube?

4

3

6

5

Explanation

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a2 → a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

3

Find the volume of a cube with side length 10.

Explanation

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

4

Find the volume of a cube given side length is .

Explanation

To solve, simply cube the side length. Thus,

5

The slant height of a cone is ; the diameter of its base is one-fifth its slant height. Give the surface area of the cone in terms of .

Explanation

The formula for the surface area of a cone with base of radius and slant height is

.

The diameter of the base is ; the radius is half this, so

Substitute in the surface area formula:

6

Find the volume of a cube with side length 10.

Explanation

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

7

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

Explanation

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

8

Find the surface area of a cube with side length .

Explanation

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

9

Find the surface area of a sphere whose radius is .

Explanation

To solve, simply remember the following formula:

10

Given the volume of a cube is , find the side length.

Explanation

To find side length, simply realize that volume is the side length cubed. Thus,

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