The ratio between the lengths of the edges of two cubes are in the rat

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

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

Answer»

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