Find the volume of the cube if: a) the area of one face is 16 cm squared b) the perimeter of one face is 20 dm

Find the volume of the cube if: a) the area of one face is 16 cm squared b) the perimeter of one face is 20 dm c) the sum of the lengths of all edges is 36 cm d) the sum of the areas of all faces is 24 dm2.

a) Given:

Cube;

S1 = 16 cm ^ 2;

Find: V.

Decision:

All the faces of the cube are equal to each other and are squares. If the area of ​​a square is 16 cm ^ 2, then its side is a = √S1 = √16 = 4 (cm).

The volume of the cube is calculated by the formula V = a ^ 3 = 4 ^ 3 = 64 (cm ^ 3).

Answer: 64 cm ^ 3.

b) P1 = 20 dm

Decision:

The perimeter of one face consists of 4 sides of a square, which means a = P1: 4 = 20: 4 = 5 (dm).

V = a ^ 3 = 5 ^ 3 = 125 (dm ^ 3).

Answer: 125 dm ^ 3.

c) The sum of the lengths of all edges is 36 cm.

Decision:

The cube has only 12 edges, then a = 36: 12 = 3 (cm).

V = a ^ 3 = 3 ^ 3 = 27 (cm ^ 3).

Answer: 27 cm ^ 3.

d) The sum of the areas of all faces is 24 dm ^ 2.

Decision:

The cube has 6 faces, so the area of ​​one is S1 = 24 ^ 6 = 4 (dm).

V = a ^ 3 = 4 ^ 3 = 64 (dm ^ 3).

Answer: 64 dm ^ 3.