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Question

The edge of a cube is increasing at the rate of 5cm/sec.How fast is the volume of the cube increasing when the edge is 12cm long

A
432cm3/sec
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B
2160cm3/sec
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C
180cm3/sec
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D
None of these
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Solution

The correct option is B 2160cm3/sec
Let velocity v=5 cm/sec
(Increasing the rate/sec is called the velocity)
dadt=5....(i)
Where a is distance and t is time.
But if a is edge of a cube, then V=a3
Differentiating w.r.t. time t, so
dVdt=3a2dadt=3a2.5=15a2=15×(12)2
=2160cm3/sec ( edge a =12 cm)

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