AP EAMCET · Maths · Application of Derivatives
If the volume of a sphere increases at the rate of \(2 \pi \mathrm{cm}^3 / \mathrm{s}\), then the rate of increase of its radius (in \(\mathrm{cm} / \mathrm{s}\) ), when the volume is \(288 \pi \mathrm{cm}^3\), is
- A \(\frac{1}{36}\)
- B \(\frac{1}{72}\)
- C \(\frac{1}{18}\)
- D \(\frac{1}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{72}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{d V}{d t}=2 \pi \mathrm{cm}^3 / \mathrm{s}\) \(\because\) Volume of sphere, \(V=\frac{4}{3} \pi r^3\) On differentiating w.r.t. \(t\), we get…
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