Question

The square on the diagonal of a cube has an area of 192 cm². Calculate
(i) The side of the cube in cm.
(ii) The total surface area of the cube in cm²

Answer 1

Side of cube = 9.8 cm

TSA of cube = 1152 sq. cm.

Explanation:

Given: The square on the diagonal of a cube has an area of 192 cm².

Let side of the cube be a, then by pythagoras theorem, we get:

2a^2 = square of diagonal = area of the square on the diagonal

2a^2 = 192

a^2 = 96

Therefore a = root of 96 = 9.8 cm

Total surface area of the cube = 6a^2 = 6 * 192 = 1152 sq. cm.

Answer 2

Answer:

1152

Explanation:

Given: The square on the diagonal of a cube has an area of 192 cm².

Let side of the cube be a, then by pythagoras theorem, we get:

2a^2 = square of diagonal = area of the square on the diagonal

2a^2 = 192

a^2 = 96

Therefore a = root of 96 = 9.8 cm

Total surface area of the cube = 6a^2 = 6 * 192 = 1152 sq. cm.