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The volume of a cube is increasing at the rate of 9 c m 3 / s e c . The rate (in cm 2 / sec ) at which the surface area is increasing when the edge of the cube is 9 c m , is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

Let, length of the edge of the cube is a , volume is V and surface area is S , then V = a 3 ⇒ d V d t = 3 a 2 d a d t d a d t = 3 a 2 … 1 Now, S = 6 a 2 ⇒ d S d t = 12 a d a d t d S d t = 12 9 × 3 9 2 = 36 9 = 4 c m 2 / s e c .

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