Question

related rates problem. see picture

Answer 1

we should prolly know a formula to find the volume of a cylindar to work with

Answer 2

\[V=pir ^{2}h\]

Answer 3

good, now take its derivative implicitly, what do we get?

Answer 4

h and pi are constants, so we really just need to focus on the r^2

Answer 5

\[\frac{ dV }{ dt }=2 \pi r \frac{ dr }{ dt } h\]

Answer 6

good, and they gave us dr/dt , we know the height, and the radius at this point in time is half its diameter

Answer 7

plug it all in and what do we end up with?

Answer 8

is dr/dt 1/1000?

Answer 9

well, its an odd construct, but we can use it as is or better define it

\[1/1000~ inch:3~minutes\]

divide each side by 3 to get

\[1/3000~ inch:1~minute\]

Answer 10

so it would look like\[\frac{ dV }{dt }= 2 \pi (1.9)(\frac{ 1 }{ 3000 })(6)\]

Answer 11

I got it. Thank you!

Answer 12

yes, that looks good to me

Answer 13

youre welcome, the trick is usually in finding a suitable relation to derive :) then filling in the knowns