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AP EAMCET2015MathematicsApplication of Derivatives

The volume of sphere is increasing at the rate of 1200 cu cm / s . The rate of increase in its surface area when the radius is 10 ~cm is

Options

  1. A120 sq cm / s
  2. B240 sq cm / s
  3. C200 sq cm / s
  4. D100 sq cm / s

Correct answer

B. 240 sq cm / s

Step-by-step solution

Let V be the volume, S be the surface area and r be the radius of the sphere. It is given that, d V d t =1200 cu cm / s and r=10 ~cm Now, Volume of sphere =V= 4 3 r^3 aligned & d V d t = 4 3 3 r^2 d r d t & 1200=4 (10)^2 d r d t & d r d t = 3 aligned and Surface Area of sphere, aligned & S=4 r^2= d S d t =4 2 r d r d t & d S d t =4 2(10) d r d t & d S d t =4 2 10 ( 3 ) & d S d t =240 sq cm / s aligned

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