Question

Express the edge length of a cube as a function of the cube's diagonal length d. Then express the area and volume of the cube as a function of the diagonal length.

Answer 1

Explanation:

d² = x² + x² + x²

d² = 3x²

d²/3 = x²

x = √(d²/3)

x = d√(1/3)

x = (d/3)√3

A = 6x²

A = 6((d/3)√3)²

A = 6(((d²/9)3)

A = 2d²

V = x³

V = ((d/3)√3)³

V = ((d³/27)3√3)

V = (d³/9)√3