calculusrate problem
posted by beth
A conical tank (with vertex down) is 10 feet acros the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

bobpursley
Let h be the depth.
Then the base radius (at the top) at depth h is 5*h/12. So volume of water is
V= 1/3 PI (5h/12)^2 h
take the derivative, set it equal to 10, solve for dh/dt when h=8
Respond to this Question
Similar Questions

Calculus
You have a conical tank, vertex down, which is 12 feet across the top and 18 feet deep. If water flows in at a rate of 9 cubic feet per minute, find the exact rate of change when the water is 6 feet deep. You know the rate of dV/dt … 
calculus
A conical tank( with vertex down) is 10 feet across the top and 18 feet deep. As the water flows into the tank, the change is the radius of the water at a rate of 2 feet per minute, find the rate of change of the volume of the water … 
calculus
Water is flowing freely from the bottom of a conical tank which is 12 feet deep and 6 feet in radius at the top. If the water is flowing at a rate of 2 cubic feet per hour, at what rate is the depth of the water in the tank going down … 
cal
A conical tank (with vertex down) is 12 feet across the top and 18 feet deep. If water is flowing into the tank at a rate of 18 cubic feet per minute, find the rate of change of the depth of the water when the water is 10 feet deep. … 
math
We did not find results for: a conical tank with its vertex down is 12 feet high and 12 feet in diameter at the top. water is being pumped in at the rate of 8 feet cubed per minute. find the rate at which the water level is rising … 
MathHow do I do this problem?
An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep. 
Math help, Please
An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep. 
Calculus
Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank increasing … 
Calculus
Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the exposed surface area of the water changing … 
math  calculus help!
An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep. 0.229 ft/min …