Homework Help: calculus

Posted by joseph on Thursday, December 27, 2012 at 11:15pm.

A water heater in the shape of a circular cylinder is standing vertically, resting on one of the round ends. The tank is 60 inches tall and has a volume of 30 gallons. If water is flowing into the tank at the rate of 5 gallons per minute, at what rate is the level of the water in the tank increasing?

calculus - Steve, Thursday, December 27, 2012 at 11:30pm
the volume of a 1" layer of water is 1/2 gal. So, when the height of the water is h inches, the volume of water is

v = 1/2 h
dv/dt = 1/2 dh/dt
5 = 1/2 dh/dt
so,
dh/dt = 10 in/min

You can go through all that pi r^2 stuff, but it's not needed here.

Answer this Question

Related Questions

College Physics - On average, an electric water heater operates for 3.4h each ...
calculus - Suppose that water is pouring into a swimming pool in the shape of a ...
math - calculus - Suppose that water is pouring into a swimming pool in the ...
Calculus - A solid is formed by adjoining two hemispheres to the ends of a right...
geometry - Find the volume of a barber's pole having the shape of a right ...
Math - Find the volume of a barber's pole having the shape of a right ...
math - A container in the shape of a right circular cylinder with no top has ...
AP Physics - You go to kitchen to boil water. You pour 280 gram of water to a ...
Math - Calculus 2 - An underground tank full of water has the following shape: ...
Geometry - 15.) Find the volume of a barber's pole having the shape of a ...

For Further Reading

First Name:
School Subject:
Answer: