Question

Find the percentage change in the lateral surface area of a cube if its edge is doubled.
( the answer given is 300%increase ) .
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Answer 1

Let the initial edge of the cube be 'l' cm.

Let the initial edge of the cube be 'l' cm.If each edge of the cube is doubled, then it becomes '2l' cm.

Let the initial edge of the cube be 'l' cm.If each edge of the cube is doubled, then it becomes '2l' cm.(i) Initial surface area = 6 l²

Let the initial edge of the cube be 'l' cm.If each edge of the cube is doubled, then it becomes '2l' cm.(i) Initial surface area = 6 l²New surface area = 6(2l)² = 6 × 4 l² = 24 l²

Let the initial edge of the cube be 'l' cm.If each edge of the cube is doubled, then it becomes '2l' cm.(i) Initial surface area = 6 l²New surface area = 6(2l)² = 6 × 4 l² = 24 l²Ratio = 6 l² : 24 l² = 1:4

Let the initial edge of the cube be 'l' cm.If each edge of the cube is doubled, then it becomes '2l' cm.(i) Initial surface area = 6 l²New surface area = 6(2l)² = 6 × 4 l² = 24 l²Ratio = 6 l² : 24 l² = 1:4Thus, the surface are increases by 4 times