Answer:
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.
