Water is running out of a conical funnel at the rate of 3 cubic inches per sec. If the funnel is 12 inches tall and has a radius of 4 inches, find the rate at which the water level is dropping when the water in the funnel is 8 inches below the rim of the funnel...

Question

jigglypuff314 · Answer

I'm just confused, could some one point me of what to solve for?
like   dV/dt   or    dh/dt   or idk :/

and maybe what some terms mean?
like does the "3 cubic inches per sec" mean that dV/dt = 3 in^3/s ? or no?

jigglypuff314 · Answer

@hartnn @SolomonZelman ? if you're not too busy, could you help please?

solomonzelman · Answer

You tagged me with hartnn as if I am on the same level. idk this staff, sorry.

hartnn · Answer

"3 cubic inches per sec" mean that dV/dt = 3 in^3/s" YES

jigglypuff314 · Answer

okay, but then what would I solve for?

hartnn · Answer

what is the volume of cone formula ?

jigglypuff314 · Answer

V = 1/3 pi r^2 h

hartnn · Answer

the radius remains constant, just the height of water changes

hartnn · Answer

so, differentiate V = 1/3 pr r^2 h 
w.r.t time t, what do u get ?

jigglypuff314 · Answer

I'm confused... how would the radius be constant?

hartnn · Answer

is the funnel changing its shape or size ?

jigglypuff314 · Answer

I suppose not...

hartnn · Answer

so the radius of cone will not change

jigglypuff314 · Answer

so dV/dt = 1/3 pi (2r) (dr/dt) (dh/dt) ?

hartnn · Answer

only the height of water changes which leads to change in volume

hartnn · Answer

but but we said r is constant, right ?

jigglypuff314 · Answer

so  dV/dt = 1/3 pi r^2 dh/dt ?

hartnn · Answer

yes!

hartnn · Answer

dV/dt = 3
r=4
find dh/dt

hartnn · Answer

'the rate at which the water level is dropping' = dh/dt

jigglypuff314 · Answer

so dh/dt = 9/16pi ?

hartnn · Answer

i suppose yes, except if i mis-read the question ....

jigglypuff314 · Answer

yeah, probably, because my answer key says it should be -27/(16pi)

hartnn · Answer

yes, i was wondering why we did not use the fact that it was 12 inches before and now its 8 inches in height

hartnn · Answer

so, change in height = dh  = 8-12

jigglypuff314 · Answer

? so dh/dt = -4 ?

jigglypuff314 · Answer

or new height = 4 ?

hartnn · Answer

i probably did a minor mistake somewhere,
let me call someone.... @jdoe0001 @ranga

ranga · Answer

|dw:1384720563186:dw|

ranga · Answer

Find the radius x (or r) as a function of h using the similar triangles ABC and DEC.

jigglypuff314 · Answer

x = 4/3

ranga · Answer

x/4 = h/12
x = 1/3h
V = 1/3(pi)x^2h = 1/3(pi)(1/9h^2)h = pi/27 * h^3
dV/dt = (pi/27) * 3h^2 * dh/dt

ranga · Answer

dV/dt = (pi/9) * h^2 * dh/dt
Substitute the values and solve for dh/dt

jigglypuff314 · Answer

okay, I got it! Thank You! :D

ranga · Answer

you are welcome.