Question

The volume of a sphere is increasing at 3 cubic centimeter per second. Find the rate of increase of the radius, when the radius is 2 cms.

Answer 1

The volume of a sphere, with radius r, is defined as

Given that \(\frac{dV}{dt}\) = 3cm³/sec and r = 2cm, we have to calculate \(\frac{dr}{dt}.\)

Differentiating (1) with respect to t, we get

\(\frac{dV}{dt}\) = 4πr²\(\frac{dr}{dt}\)

Substituting the values, we get