Question

Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 square root 2 inches.

Answer 1

Answer on Question #57867 – Math – Geometry

Question

Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 square root 2 inches.

Solution

Volume = V.

A cube is a regular hexahedron. If length of cube's edge is $a$, then volume will be $V = a^3$.

Triangle $\Delta ABC$ is right and $AB = BC = a$. AC is a diagonal of a cube face and the hypotenuse of $\Delta ABC$.

By Pythagorean theorem: $AB^2 + BC^2 = AC^2 \rightarrow 2 * a^2 = (8\sqrt{2})^2 = 64 * 2 \rightarrow a^2 = 64$

$$a = \sqrt{64} = 8$$ $$V = a^3 = 8^3 = 512$$

**Answer**: $V = 512$ cubic inches.

www.AssignmentExpert.com