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

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)

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