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Find the rate of change of volume of the cube when the side of the cube is 10 cm. It is known that the side changes at the rate of 4 cm/s.

  1. 800 cm3/s
  2. 1000 cm3/s
  3. 1200 cm3/s
  4.  500 cm3/s

Answer (Detailed Solution Below)

Option 3 : 1200 cm3/s
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Detailed Solution

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Concept:

The rate of change of the value of a function f(x) with respect to a variable t, is given by: 

Calculation:

Given the side of the cube L = 10cm and  = 4 cm/s

Now volume of the cube V = L3 

 =  × 

 =  × 4

 = 3L2 × 4

 = 12 × 102 

 = 1200 cm3/s

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