Q. 74.0( 142 Votes )

# If each edge of a cube is doubled,

(i) how many times will its surface area increase?

(ii) how many times will its volume increase?

Answer :

(i) ∵ Surface Area of a Cube SA= 6(Side)^{2}

If Side is doubled then New Surface Area,

SA' = 6(2×Side)^{2}

= 4× 6(Side)^{2}

= 4 × SA

∴ SA of new Cube will be 4 times of SA of Original Cube.

(ii) ∵ Volume of a Cube V= (Side)^{3}

V'= (2× Side)

^{3}

= 8× (Side)

^{3}

= 8× V

∴ Volume of new Cube will be 8 times the Volume of Original Cube.

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