Related Rates cylinder problem

[Mitchtwitchita]

A cylinder is placed in oven where both the height and base radius expand at 0.1 mm/min. When the height is 250 mm and the radius of the base 30 mm, the volume is expanding at ...mm3 /min. (Answer to nearest whole number)

r=30, h=250, dr/dh=0.1, dh/dt=0.1

dV/dt = (pi)r^2(dh/dt) + 2rh(dr/dt)
=(pi(30)^2(0.1) + 2(30)(250)(0.1)
=1783

Can anybody please show me where I'm going wrong with this one?

 

[rocomath]

$$V=\pi r^2h$$

You're missing a pi term!

$$\frac{dV}{dt}=\pi[2hr\frac{dr}{dt}+r^2\frac{dh}{dt}]$$

 

[Mitchtwitchita]

Thanks roco!