Question

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

Answer 1

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

Answer 2

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)