Can someone help me with this please?
Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the funnel is initially full, how long will it take for it to be one-third-full? What is the height of the water level? Assume the radius to be 6 inches and the altitude of the cone to be 15 inches.
Assumed answers in my textbook says 31.4 mins and 10.4 inches but I don't know how to solve it.

Question

Can someone help me with this please?
Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the funnel is initially full, how long will it take for it to be one-third-full? What is the height of the water level? Assume the radius to be 6 inches and the altitude of the cone to be 15 inches.
Assumed answers in my textbook says 31.4 mins and 10.4 inches but I don't know how to solve it.

mjdennis · Answer

So, to get started, what is the equation for the volume of this cone?|dw:1464960950597:dw|

phi · Answer

Are you able to find the volume of the cone? or are you stuck ?

iane12 · Answer

i was able to find the volume of the whole funnel but i can't find the the water's volume and the time

phi · Answer

what did you get for the total volume ?

iane12 · Answer

569.49

phi · Answer

that seems a bit off.  If you leave it in terms of pi (i.e. don't multiply by pi, just show pi)
what do you get ?

iane12 · Answer

oh sorry. i got 180pi

phi · Answer

yes, and that is 565.49 (approximately).  I guess you had a typo.

the next part is a bit tricky.  If they funnel is ⅓ full, how much water leaked out ?

phi · Answer

and in problems like this, it's always good to include the units (just to make sure we don't confuse different units).  in this case the volume is in cubic inches.