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Question

The edge of a cube is increasing at the rate of 7cm/sec. How fast is the volume of the cube increasing when the edge is 10cm long?

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Solution

Suppose edge of cube =a, time =t, volume =v
V=a3
According to question, at time t increase in rate edge of cube
dadt=7cm/sec
at time t increase in rate volume
dvdt=ddta3
dvdt=dda×a3×dadt
dadt=3a2×7=21a2
Increase in rate of volume of the cube when a=10cm
dvdt=21×102=2100cm3/sec

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