AP EAMCET · Maths · Application of Derivatives
If the volume of a sphere is increasing at the rate of \(12 \mathrm{c}. \mathrm{c}. / \mathrm{sec}\), then the rate (in \(\mathrm{sq}. \mathrm{cm} / \mathrm{sec}\) ) at which its surface area is increasing, when the diameter of the sphere is 12 cm is
- A \(2\)
- B \(3\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\( r = \frac{D}{2} = \frac{12}{2} = 6 \text{ cm} \) \( \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} \) \( 12 = 4\pi (6)^2 \frac{dr}{dt} \implies \frac{dr}{dt} = \frac{12}{144\pi} = \frac{1}{12\pi} \text{ cm/sec} \) \( \frac{dA}{dt} = 8\pi r \frac{dr}{dt} \)…
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