MathHow do I do this problem?
posted by Mark .
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.

MathDamon can you help me? 
Mark
Do you know what kind of formula I could use to solve this?

MathHow do I do this problem? 
Damon
sure
change in volume = surface area * change in depth
or
dV = pi r^2 dh
dV/dt = pi r^2 dh/dt = 12 ft^3/min
so
dh/dt = 6/(pi r^2)
if r = 7, h = 24
or
r = (7/24)h = (7/24)(10) = 70/24
so
dh/dt = 6 / [ pi (70/24)^2 ] 
MathHow do I do this problem? 
Steve
Hmmm. I get
r = 7/24 h
so, dr = 7/24 dh
r = 35/12 when h=10
v = 1/3 pi r^2 h
using the product rule,
dv = 1/3 pi (2rh dr + r^2 dh)
12 = pi/3 (2*(35/12)(10)(7/24 dh)+(35/12)^2 dh)
12 = 1225/144 pi dh
dh = 1728/1225 pi
= 12^3/35^2 pi
Maybe you can figure out whether one of us is correct.
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 … 
Math
A conical tank (with its vertex down) is 8 feet tall and 6 feet across its diameter. If water is flowing into the tank at the rate of 2 feet3/min, find the rate at which the water level is rising at the instant when the water depth … 
math  calc
A conical water tank with vertex down has a radius of 12 feet at the top and is 26 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet … 
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. … 
Calculus (math)
A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet … 
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. 
math
A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If water flows into the tank at a rate of 10 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17 feet … 
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 …