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JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the surface area of a sphere of radius \(r\) is increasing uniformly at the rate \(8\, cm^2/s\), then the rate of change of its volume is
- A constant
- B proportional to \(\sqrt r \)
- C proportional to \(r^2\)
- D proportional to \(r\)
Answer & Solution
Correct Answer
(D) proportional to \(r\)
Step-by-step Solution
Detailed explanation
\(V = \frac{4}{3}\pi {r^3}\,\, \Rightarrow \frac{{dV}}{{dt}} = 4\pi {r^2}.\frac{{dr}}{{dt}}\,\,\,\,\,\,\,\,\,\,.....\left( i \right)\) \(S = 4\pi {r^2} \Rightarrow \frac{{dS}}{{dt}} = 8\pi r.\frac{{dr}}{{dt}}\)…
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