If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing,is

Question

Dr. Abubacker · Accepted Answer

(d)
Given that, $\frac{dV}{dt} = k$ (say)
$\because\ \ \ V = \frac{4}{3}\pi R^{3}$
$\Rightarrow \ \ \ \frac{dV}{dt} = 4\pi R^{2}\frac{dR}{dt}$
$\Rightarrow \ \ \ \frac{dR}{dt} = \frac{k}{4\pi R^{2}}$
$\Rightarrow$ Rate of increasing radius is inversely proportional to its surface area

Q. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing,is

Explanation

Reviewed by Dr. Abubacker

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