The total surface area of a cube is 150 square centimeters. What is the volume of the cube… — Armed Services Vocational Aptitude Battery (ASVAB)

The total surface area of a cube is $150$ square centimeters. What is the volume of the cube, in cubic centimeters?

Answer: 125 cubic centimeters

125

The correct answer is derived by first identifying the side length of the cube. Given the total surface area is

150

square centimeters, we divide by

6

to find the area of a single face (

25

square centimeters). The square root of

25

gives a side length of

5

centimeters. Finally, cubing this side length (

5 \times 5 \times 5

) results in a total volume of

125

cubic centimeters.

Use the total surface area to find the area of a single face of the cube.

150 \div 6 = 25

square centimeters.

A cube has exactly

6

identical square faces. Dividing the total surface area by

6

isolates the area of just one face (

s^2

Determine the length of one edge of the cube.

s = \sqrt{25} = 5

centimeters.

Because the area of a square face is the side length squared (

s^2

), taking the square root gives the side length.

Calculate the total volume of the cube.

V = 5^3 = 125

cubic centimeters.

The formula for the volume of a cube is the side length cubed (

V = s^3

Converting between the surface area and volume of a 3D figure by finding the missing dimension.

Estimated Time:45s

Question