Answer to Question #145767 in Calculus for liam donohue

Question

A Spherical balloon is being inflated.
Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V=4πr33.

Answer:


Find the rate of change of V with respect to r at the instant when the radius is r=5.

Answer:

Answer 1

$\begin{aligned} a) \quad V &= \frac{4}{3} πr^3\\ \\ \dfrac{dV}{dr} &= 3(\frac{4}{3}) πr^{3-1}\\ \\&= 4πr^2\\ \\ \\ b) \dfrac{dV}{dr}_{|r= 5|}&= 4πr^2\\ \\ &= 4π(5)²\\ \\ &= 100π \end{aligned}$