Find the volume of a cube if the perimeter of one of its faces is 20 cm.

A cube (hexahedron) is a regular polyhedron, each face of which is a square.

1) Find the edge of the cube.

Based on the definition of a cube, each face is a square. Hence, the edge of the cube is the side of the square. Find the side of a square if its perimeter is known.

Let’s write the formula for the perimeter of the square:

P = 4 × a,

where P is the perimeter, and is the length of the side of the square.

From the formula for the perimeter of a square, we express its side:

a = P ÷ 4.

We calculate the length of the side of the square (the edges of the cube):

a = 20 ÷ 4 = 5 cm.

2) Find the volume of the cube.

To calculate the volume of a cube, you need to raise its side to the third power. Let’s write a formula for calculating the volume of a cube:

V = a³,

where a is the edge of the cube, V is the volume of the cube.

Substituting the value of the edge of the cube into the formula, we find its volume:

V = 5³ = 125 cm³.

Answer: the volume of the cube is 125 cm³.