(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

2. Relevant equations

V=1/3 pi(r)^2*h

relationships:

4/2r=6/h

therefore,

r=1/3h

Substituting h for r:

V=1/3 pi (1/3h)^2(h)

V=pi/27(h)^3

V'=dv/dt= pi/27 (3h)^2dh/dt

dv/dt=pi/27 (3*200)^2(20)

since the cone is leaking we have to find:

dv/dt-6500=pi/27(3*200)^2(20)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Rate water has to be added to Leaking cone

**Physics Forums | Science Articles, Homework Help, Discussion**