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TS EAMCET · Maths · Application of Derivatives

The radius of a sphere is changing. At an instant of time the rate of change in its volume and its surface area are equal. Then the value of radius at that instant is?

  1. A 1
  2. B 2
  3. C \(\frac{3}{2}\)
  4. D 3
Verified Solution

Answer & Solution

Correct Answer

(B) 2

Step-by-step Solution

Detailed explanation

Given that, at any instant of time Rate of change in volume w.r.t. time \(=\) rate of change in surface area w.r.t. time i.e., \(\frac{d v}{d t}=\frac{d s}{d t}\) \(\ldots(i)\) Volume of sphere of radius \((r), V=\frac{4}{3} \pi r^3\) Differentiating w.r.t, ' \(t\) ', we get…