The surface area of a cube is 384 square inches. What is the volume of the cube????

A. 8 cubic inces
B. 16 cubic inches
C. 256 cubic inches
D. 512 cubic inches

To find the volume of a cube, you need to know the length of one side. Since only the surface area is given, we need to find the length of one side of the cube first.

The formula for the surface area of a cube is 6s^2, where s is the length of one side.

Given that the surface area is 384 square inches, we can set up the equation: 6s^2 = 384.

Divide both sides by 6: s^2 = 64.

Take the square root of both sides to solve for s: s = 8.

Now that we know the length of one side is 8 inches, we can find the volume.

The volume of a cube is calculated by cubing the length of one side. So, the volume is 8^3 = 512 cubic inches.

Therefore, the correct answer is option D. 512 cubic inches.

To find the volume of a cube, you need to know its surface area.

First, let's find the length of one side of the cube.

The formula for the surface area of a cube is 6s^2, where s represents the length of one side.

Given that the surface area is 384 square inches, we can set up the equation:

384 = 6s^2

To isolate s^2, divide both sides of the equation by 6:

384/6 = s^2

64 = s^2

Next, take the square root of both sides of the equation to solve for s:

√64 = √s^2

8 = s

Now that we know the length of one side of the cube is 8 inches, we can find its volume.

The formula for the volume of a cube is s^3, where s represents the length of one side.

Plug in the value of s:

V = 8^3

V = 8 x 8 x 8

V = 512 cubic inches

Therefore, the correct answer is D. 512 cubic inches.

Let the side length be a.

The area is 6 a^2 = 384, so
a^2 = 64

That should tell you what the value of a is.

The volume of the cube is a^3. It is one of your choices. Do the numbers.