Volume Of A Cube - High School Math

One face of a cube has an area of 64 cm square – What is the volume of this cube?

Answer : 512 cm cubed

In order to calculate the volume of a cube, the length, height and width of the cube must be known since the formula for finding the volume is:
V = l w h
The problem does not provide information about the length, width or height; therefore they must be calculated using the information we were given about the area.

In this problem, we are given the area of one face. We know that the formula for calculating an area for any two dimensional figure is:
A = l w
Since each face of a cube is constructed from a square, then we know that the length and width of this square must be the same and by multiplying the two, the area can be found.

Lets apply what we have:
64 cm square = l w
Since we know that the length and width must be equal for a square, we can take the square root of the area in order to calculate the length of width:

square root of 64 = 8

Therefore, the length and width of each face is 8 cm. Therefore, the height of this cube will also be
8 cm. The volume can now be calculated as follows:

V = (8cm)(8cm)(8cm) = 512 cm cubed.

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