# Thread: expanding metal (related rate)

1. ## expanding metal (related rate)

A metal rod is in the shape of a right circular cylinder. As it is heated its length is changing at a rate off 0.2 mm/min and its radius is changing at a rate of 0.05 mm/min. How fast is the volume changing when the rod is 40cm long and 3 cm in diameter?

This one has me completely lost.

2. Originally Posted by hotdogking
A metal rod is in the shape of a right circular cylinder. As it is heated its length is changing at a rate off 0.2 mm/min and its radius is changing at a rate of 0.05 mm/min. How fast is the volume changing when the rod is 40cm long and 3 cm in diameter?

This one has me completely lost.
$V=\pi r^2h$

$\frac{dV}{dt}=\pi(r^2\frac{dh}{dt}+h(2r\frac{dr}{d t}))$

$\frac{dh}{dt}=.2$

$\frac{dr}{dt}=.05$

$h=400$

$r=15$