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.

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step-by-step explanation: