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Question

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


A

750cm3/sec

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B

75cm3/sec

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C

300cm3/sec

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D

150cm3/sec

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E

25cm3/sec

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Solution

The correct option is A

750cm3/sec


Step 1. Given data:

The variable edge of the cube, dxdt=10cm/sec

The edge of the cube, x=5cm

Step 2. Formula used:

The volume of the cube, V=x3.....1

Step 3. Finding the increase in the volume of the cube:

Differentiating both sides of the equation 1, we get

dVdt=3x2(dxdt)dVdt=3(5)2(10)dVdt=750cm3/sec

Hence, the volume of the cube is increasing at the rate of 750cm3/sec

Hence, option A is correct.


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