Question

The ratio between the lengths of the edges of two cubes is in the ratio 3: 2. Find the ratio between their:
(i) total surface area
(ii) volume.

Answer 1

Ratio in edges of two cubes = 3:2

Let edge of first cube = 3x

Then edge of second cube = 2x

(i) Now total surface area of first cube = 6 x (3x)² = 6 x 9x² = 54x²

and of surface area of second cube = 6 x (2x)² = 6 x 4x² = 24x²

Ratio = 54x²: 24x² = 9:4

(ii) Volume of first cube = (3x)³ = 27x³

and second cube = (2x)³ = 8x³

Ratio = 27x³: 8x³ = 27 :8