Rates involving two or more variables (1 Viewer)

[atakach99]

The radius of a cylindrical pipe 2 m long expands with heat at a constant rate of 1.2 x 10 ^-3 mm/s. Find the rate at which the volume of the pipe will be increasing when its radius is 19 mm.

plz help
thnks

 

[tacogym27101990]

ok so we need to find dv/dt
and we know dr/dt and we can find an expression for dv/dr

and dv/dt= dv/dr . dr/dt

and v=pir²h
dv/dr= 2pirh
sub in r=19 and h=2000 as they need to be in the same units

then times that by 1.2X10^-3mms^-1

answer i got is about 287mm³s^-1