MHT CET · Maths · Application of Derivatives
The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm , after 2 minutes its radius becomes 9 cm , then radius of balloon after 4 minutes is
- A 12 cm
- B 14 cm
- C 15 cm
- D 18 cm
Answer & Solution
Correct Answer
(C) 15 cm
Step-by-step Solution
Detailed explanation
\( \frac{dV}{dt} = kA \) \( \frac{d}{dt}\left(\frac{4}{3}\pi r^3\right) = k(4\pi r^2) \)
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