Asked by Jordan

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 the water is 7
meters deep

Answers

Answered by Jordan
is the answer 8/49pi= 0.052 meters per minute
Answered by Steve
I get dV/dt = pi/16 h^2 dh/dt
giving
2 = 49pi/16 dh/dt
or
dh/dt= 32/49pi

One of us has a factor of 2 out of place. Could be me ...
Answered by Reiny
I did not get that

Let the height of the water be h m and the radius of the water level be r m
by ratios:
r/h = 5/20 = 1/4
r = h/4

V = (1/3)πr^2 h = (1/3)π(h^2/16)(h)
= (1/48)π h^3
dV/dt = (1/16)π h^2 dh/dt
so when dV/dt = 2, h = 7
2 = (1/16)π(49) dh/dt
2(16)/(49π) = dh/dt
= 32/(49π)
= appr. .208 m/min
Answered by Jordan
WELL I HAVE THIS

v=1/3pi*r^2h
v=1/3pi*r2(4r)
v=4/3pi*r^3
dv/dt=4pi*r^2
2=4pi(7/4)^2
2=49pi/4 * dr/dt
dr/dt= 8/49pi = 0.052 meters per minute
Answered by Reiny
You have found the rate at which the rate is changing.

Unfortunately, your question asked for how fast the height is changing.
Answered by Reiny
should say:


You have found the rate at which the radius is changing.

Unfortunately, your question asked for how fast the height is changing.

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