7.If each edge of a cube is doubled,

(i) how many times will it be surface area increase?

(ii) how many times will its volume increase?

(i) how many times will it be surface area increase?

(ii) how many times will its volume increase?

Let the edge of the cube = x cm

As per the question, edge is doubled so the new edge = 2x cm

(i)We have original surface area =\( 6x^2 cm^2\)

And, the new surface area = \(6(2x)^2 = 6 \times 4\times2 = 24\times2\)

∴ Ratio = \(6x^2 : 24x^2 = 1 : 4\)

Hence, the new surface area will be four times the original surface area.

(ii)We have, original volume of the cube = \(x^3 cm^3\)

And, the new volume of the cube = \((2x)^3 = 8x^3 cm^3\)

∴Ratio =\( x^3 : 8x^3 = 1 : 8\)

Hence, the new volume will be eight times the original volume.