Question

What is the length of a diagonal of a cube with a side length of 6 inches?

Answer 1

d = 6√3 inches ≈ 10.40 inches

Explanation:

d² = a² + c²

= 36 + 72

= 108

d = √108

= √3×36

= √3×6²

= 6√3 inches

= 6×1.73 inches

= 10.38 inches

≈ 10.40 inches

Answer 2

10.4 inches

Explanation:

To find the length of the diagonal through the cube, we use the Pythagorean theorem again with legs sqrt(72) and 6, looking for the hypotenuse

a^2 + b^2 = c^2

6^2 + (sqrt(72)^2) = c^2

36 +72 = c^2

108 = c^2

Take the square root of each side

sqrt(108) = sqrt(c^2)

sqrt(108) = c

10.39230485 =c

Rounding to the nearest tenth

10.4 = c