Question

related rates problem need help stat! Please!
A cylindrical tank with radius 5m is being filled with water at a rate of 3m/min. How fast is the height of the water increasing.

Answer 1

what is the formula for the volume of a cylindar?

Answer 2

I believe the formula is pi r^2h

Answer 3

Thank you for helping me out! I appreciate it. how do i go about solving this type \of problem.

Answer 4

good, then lets take an implicit derivative wrt.time of:\[V=\pi r^2 h\]

Answer 5

\[V=\pi r^2 h\]
\[V'=2r~\pi r' h+\pi r^2 h'\]
since r is a constant at 5, r' is 0
\[V'=\pi r^2 h'\]
they give us the change in volume to be 3, and r=5
\[3=\pi 5^2 h'\]
solve for h'

Answer 6

Thank you so much sorry i couldn't reply back my computer froze.But i see what you did there but to solve for h what would i do?

Answer 7

Sorry about that i just reread the problem and it reads 3m^3 not 3m. sorry for the typo.

Answer 8

thats still a volume rate ... so 3 is fine

Answer 9

if you want to include it then

3m^3 = (5m)^2 pi h'

3m^3
--------- = h'
(5m)^2 pi



3 m
--------- = h'
25 pi

Answer 10

okay that's great I thought that that would effect the result of the problem.

Answer 11

nah, but its prolly a good idea to include it to make sure the dimensions pan out :)

Answer 12

oh okay so when solving for a problem like this could you just leave it in a fraction or should you simplify the answer?

Answer 13

depends on who is grading it really ...

Answer 14

i usually give exact and then approximate it as a decimal:\[this\approx n.xxx\]

Answer 15

well in that case my professor rarely stresses simplifying so i think that leaving it in a fraction is fine. Thank you for your help amistre64. have a great day!:)

Answer 16

youre welcome, and good luck :)

the strategy i use is to find a formula that can be derived; take implicits and start filling in the parts that can be knowned