Question

The formula for the volume of a cone is V=(1/3)pi r^2h. Find the rate of change formula if dr/dt is 3 inches per minute and h=3r when (a) r=3 inches and (b) r=9 inches

Answer 1

This what I got so far... Is this right?

V=(1/3) pi r^2h
d/dt[V] = (1/3) pi r^2h
dV/dt = (1/3) 2pi r dr/dh *h
dV/dt = (1/3) 2pi(3)(3)(3)(9)

My answer is: dV/dt = 162 pi

Answer 2

Correction: *Find the rate of change of the volume if...

Answer 3

start by substituting 3r for h so the volume is

\[V = \frac{1}{3} \times \pi \times r^2 \times 3r~~~or~~~ V = \pi r^3\]

then differentiate V with respect to r dV/dr

next using the change rule

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

hope it helps

Answer 4

when you get the equation for dV/dt substitute r = 3 and evaluate

then the same for r = 9

Answer 5

oops chain rule... note change rule