Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 13 feet high? (The volume of a right circular cone with height, h, and radius of the base, r, is given by : V=1/3pir^2h)

Question

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 13 feet high?  (The volume of a right circular cone with height, h, and radius of the base, r, is given by : V=1/3pir^2h)

anonymous · Answer

$$V=1/3\Pi r^2h$$ This is the formula written more properly.

zepdrix · Answer

Hmm let's see if we can successfully label all the pieces.

anonymous · Answer

:)

zepdrix · Answer

Gravel is being added to the pile at a rate of 10ft^3/min
That is the rate at which the volume is changing.
$$\frac{ dv }{ dt }=10ft^3/\min$$

anonymous · Answer

right

zepdrix · Answer

|dw:1352141690856:dw|