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Question
If each edge of a cube is doubled, how many times will its surface area increase?
Solution
Let the side of cube = l
Then surface area of the old cube = 6l2 ...(i)
If each edge of the cube is doubled, then side = 2 × l
Then surface area of the new cube = 6(2l)2 = 6 × 4l2
= 4 × 6l2 ...(ii)
From equations (i) and (ii),
Surface area of new cube = 4 × surface area of old cube
Therefore, in this situation, the surface area of the cube will increase four times.
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