Question

What is the length of a diagonal of a cube with a side length of 6 inches? Length of a diagonal of the face: 6 squared + 6 squared = c squared. 36 + 36 = c squared. 72 = c squared. StartRoot 72 EndRoot = c. Use the diagonal of the face of the cube and the side length of the cube to find the length of the diagonal of the cube. Round to the nearest tenth of an inch. The diagonal through the interior of the cube is about inches.

Answer 1

10.4 inches

Step-by-step explanation: got it right on ed :)

Answer 2

10.4 inches

Explanation:

As your problem statement tells you, the face diagonal length is √72 = 6√2. The space diagonal length is computed using a second application of the Pythagorean theorem. It will be the hypotenuse of the right triangle whose legs are the face diagonal and the edge of the cube.

d² = 6² +(6√2)² = 36 +72 = 36×3

d = √(36×3) = 6√3 ≈ 10.4

The interior diagonal is about 10.4 inches long.