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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?

Answer :

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.