What is the volume of a cube that has a face diagonal of 5 cm? (to the nearest whole number)

To calculate for the volume of the cube, we need first to determine the lengths of the sides. This can be calculated by using the Pythagorean theorem.

e² + e² = 5² = 25

The value of e from the equation is equal to 3.54 cm. The volume of a cube is equal to the cube of the length of the edge.

V = e³

Substituting,

V = (3.54) ³ = 44.19 cm³

Answer: 44.19 cm³

A cube has equal size of edges. Since it has a face diagonal of 5cm then using Pythagoras theorem s² + s² = 5², where s is the side of the cube.

Therefore, 2s²=25

s² = 12.5

s = √12.5 = 3.536 cm

The volume of a cube is s³ (s*s*s) = 3.536³ = 44.212 cm³,

Therefore, the volume of the cube will be 44 cm³ (nearest whole number)