CALCULUS  PLEASE HELP
posted by Anonymous .
Water is flowing at a rate of 50 cubic meters per minute into a holding tank shaped like a cone, sitting vertex down. The tank's base diameter is 40 m and a height of 10 m.
Write an expression for the rate of change of the water level with respect to time, in terms of h (the water's height in the tank).

using similar triangles, the radius of the water surface at height h can be found
r/h = (40/2)/10 = 2
so, r = 2h
v = 1/3 π r^2 h
= π/3 (2h)^2 h
= 4π/3 h^3
dv/dt = 4π h^2 dh/dt
50 = 4π h^2 dh/dt
dh/dt = 25/(2πh^2)
Respond to this Question
Similar Questions

Calculus
Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top … 
Calculus
Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top … 
Calculus (pleas help!!!)
Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top … 
AP CALCULUS!!! HELPP
related rates: the base of a pyramidshaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate … 
AP CALCULUS!! HELPPP URGENT
related rates: the base of a pyramidshaped tank is a square with sides of length 12 meters, and the vertex pyramid is 13 meters above the base. the tank is filled to a depth of 5 meters, and water is flowing into the tank at the rate … 
calculus  please help!
Water is leaking out of an inverted conical tank at a rate of 13200 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is … 
Calculus (Help please)
A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when … 
Math (Calculus)
A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when … 
Math (Calculus)
A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when … 
calculus(related rates)
Water is leaking out of an inverted conical tank at a rate of 12200 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 15 meters and the diameter at the top …