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

If Side is doubled then New Volume of Cube,
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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