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.
New surface area =6(2l)2
=24l2
= 4 × 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
Clearly, the volume of the cube will be increased by 8 times.