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Question

An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase when the edge is 5cm long?


A

750cm3/s

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B

75cm3/s

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C

150cm3/s

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D

25cm3/s

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Solution

The correct option is A

750cm3/s


Explanation for the correct option:

Calculate the increased volume of the cube : (when the edge is 5cm long)

Let the edge of the cube be “x” cm and edge of a variable cube is increasing at the rate of 10 cm/s.

dxdt=10cm/s

VolumeV=x3differentiatewithrespectto"t"dvdt=3x2dxdtdvdtx=5cm=3(5)2×10=750cm3/sec

Hence, the correct option is A.


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