Differential Calculus
posted by Patricia .
From a faucet, a constant inflow of water is to fill a conical vessel 15 feet deep and 7.5 feet in diameter at the top. water is rising at the rate of 2 feet per minute when the water is 4 feet deep. what is the rate of inflow in ft^3/min?

Differential Calculus 
Reiny
Make a sketch of the cone with some water in it.
Let the depth of the water be h ft, and the radius of the water level be r ft
by similar triangles:
r/h = 3.75/15
3.75h = 15r
h = 4r or r = h/4
V = (1/3)π r^2 h
V = (1/3)π(h^2/16)h
V = (1/48)π h^3
dV/dt = (1/16)π h^2 dh/dt
given: when h = 4 , dh/dt = 2
dV/dt = (1/16)π (16)(2) = 2π
The rate of inflow is 2π ft^3/min
check my arithmetic, I did not write it out on paper first.
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 … 
calculusrate problem
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. 
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
They're actaully 2 question :D 1.find the rate of change of the distance between the orgin and a moving point on the graph of y=x^2+1 if dx/dt=2 centimeters per second when x=1. 2.A triangular trough is 12 feet long and 3 feet across … 
math
a vessel comtaining water has the shape of an inverted circular cone of base radius 5 feet and height 10 feet.the water flow from the apex of the cone at a constant rate of 3 cubic feet per minute.how fast is the water lavel rising … 
Calculus
A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how … 
Math
A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how … 
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 … 
Differential calculus
reservoir has the shape of a rightcircular cone. The altitude is 10 feet, and the radius of the base is 4 ft. Water is poured into the reservoir at a constant rate of 5 cubic feet per minute. How fast is the water level rising when …