Question

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80mm?

Answer 1

well isn't this a case of

\[\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt}\]

\[V = \frac{4}{3} \pi r^3....so.... \frac{dV}{dr} =4\pi r^2\]

then
\[\frac{dV}{dt} = 4\pi r^2 \times 4\]

now substitute r = 40 and find the rate of change in the volume with respect to time.