The rate of change of surface area of cube is 216 cm2/s and that of the side of the cube is 2 cm/s, find the length at that time.

  1. 9
  2. 12
  3. 16
  4. 20

Answer (Detailed Solution Below)

Option 1 : 9
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Detailed Solution

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Calculation:

Given that the side (L) of the cube changes at the rate = = 2 cm/s

Surface Area of the cube V = 6L2

Rate of change of Surface Area A =

 = ​​

 =  = 24L

As  = 216 cm2/s 

216 = 24 × L

L =  = 9 cm

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