Question

The volume of a cube is related to the area of a face by the formula V = A 3 2 . What is the volume of a cube whose face has an area of 81 cm2?

Answer 1

Explanation:

We have V=A3/2

We know that A = 100cm2, so just plug the area into the equation:

V = 1003/2

= 1002/2 * 1001/2

= 100 * √(100)

= 100 * 10 = 1000 cm3

Therefore, the area is 1000cm3

Another way to solve the problem is to figure out what the side length is from the area. Since the area is 100cm2, and we know that area of a cube face is s2 (where s is the length of the side), we can figure out the side length first like this:

s = √(100cm2)

s = 10cm

Then we can calculate volume using V = s3 = 1000 cm3