Find the volume of a cube if the area of the bottom face is 64 dm.kv.

Any face of a cube, including the bottom one, is a square. The area of a square is found by the following formula:
S = a², where a is the side of the face.
Let us express the side of the face from this formula:
a = √S.
Find the side length:
a = √64 = 8 dm.
All sides of the cube are equal, so its volume is sought using the following formula:
V = a³.
Let’s find the volume of this cube:
V = 8³ = 512 dm³.
Answer: the volume of a cube is 512 cubic decimeters.