What is the length of diagonal d of a cube that is 10 on each edge? Round your answer to the nearest tenth of an inch.

17.3 in

Step-by-step explanation:

(a) Diagonal on a face

First, we calculate the diagonal f on a face of the cube.

a² + a² = f²

f² = 2a²

(b) Diagonal of the cube

Consider the triangle made by the diagonal d, diagonal f, and the edge of the cube

d² = f² + a²

Substitute the value of f² d² = 2a² + a² = 3a²

Take the square root of each side d = a√3

Substitute the value of a d = 10√3 = 10 * 1.732 = 17.3 in

The diagonal of the cube is 17.3 in.