Question

The area of a square on the diagonal of a cube is 48 cm². Each edge of the cube is ______.

Options

• 2 cm

• 4 cm

• 6 cm

• 8 cm

Answer 1

The area of a square on the diagonal of a cube is 48 cm². Each edge of the cube is 4 cm.

Explanation:

The diagonal of a cube with edge a is given by \[d = a\sqrt{3}\], and the area of the square on this diagonal is \[d^2 = (a\sqrt{3})^2 = 3a^2\]. Given that this area is 48 cm², we have 3a² = 48, which gives a² = 16 and thus a = 4 cm.