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Question

Mathematics Question on Volume and Capacity

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) Let initially the edge of the cube be l.
Initial surface area = 6 l 2
If each edge of the cube is doubled, then it becomes 2l.2l.
New surface area =6(2l)26(2l)^ 2
=24l= 24 l2
= 4 ×\times 6 l 2
Clearly, the surface area will be increased by 4 times.


(ii) Initial volume of the cube = l 3
When each edge of the cube is doubled, it becomes 2 l.
New volume =(2l)3=8l3=8×l3= (2l)^3 = 8l^ 3 = 8 \times l^ 3
Clearly, the volume of the cube will be increased by 8 times.