The perimeter of the cube face is 32 cm, find the surface area of the cube, find the volume of the cube.

We have the perimeter of a cube face, it is known that a cube face is a square, we can find the length of the cube edge:
P = 4a => a = P / 4 = 32/4 = 8 cm.
To find the surface area of a cube (S = 6S1), we need to find the face area of a cube to begin with:
S1 = a ^ 2 = 64 cm2.
Cube surface area:
S = 6S1 = 6 * 64 = 384 cm2.
Let’s find now the volume of the cube as:
V = a ^ 3 = 8 ^ 3 = 512 cm3.
Answer: cube surface area: 384 cm2; cube volume: 512 cm3.