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?
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?
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(i) Let initially the edge of the cube be l. Initial surface area = 6l2
If each edge of the cube is doubled, then it becomes 2l.
New surface area = 6(2l)2 = 24l2 = 4 × 6l2
Clearly, the surface area will be increased by 4 times.
(ii) Initial volume of the cube = l3
When each edge of the cube is doubled, it becomes 2l.
New volume = (2l)3 = 8l3 = 8 × l3
Clearly, the volume of the cube will be increased by 8 times.
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