# Calculus

A water tank in the shape of a right circular cylinder has a volume that is increasing at the rate
of 300pi cubic centimeters per hour. If the height is decreasing at the rate of 15 centimeters per hour,
find the rate at which the radius is changing when the radius is 20
centimeters and the height is 30 centimeters.

1. 👍 0
2. 👎 0
3. 👁 204
1. v = 1/3 pi r^2 h
dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt)
Now just plug in
dv/dt = 300pi
dh/dt = -15
r=20
h=30
and solve for dr/dt

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### calculus

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

asked by joseph on December 27, 2012
2. ### MATH WORD PROBLEM HELP PLEASE

A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume of 320pi cubic feet. What is the diameter, in feet, of the water tank?

asked by Anonymous on April 14, 2015
3. ### college algebra

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and volume of the tank is 5pie cubic feet. Find, to the nearest thousandth of a foot the length of the radius x.

asked by Missy on April 16, 2012
4. ### Calculus

A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the

asked by ANON on July 18, 2016
5. ### Calculus

A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the

asked by ANON on July 17, 2016
1. ### calculus

A tank in the shape of a right circular cylinder is filled with water (62.5 lb/ft3). It has a height of 8 ft and a diameter of 10 ft. How much work is required to pump all the water to a spout that is 3 ft above the top of the

asked by ANON on July 18, 2016
2. ### college

A tank for storing water is conical in shape, with maximum radius 20 m and maxi­mum depth 15 m. The large, circular end of the tank points vertically upwards and is open to the air. It is known that the volume of water in the

asked by Pankaj on October 19, 2015
3. ### Math

A cylinder fish tank has a volume of 301.44, a rectangular fish tank as a volume of 300, and a triangular prism tank has a volume of 253.75. Obviously the cylinder tank holds more water, but is there a mathematical reason why

asked by Ben on April 22, 2015
4. ### Math - Calculus 2

An underground tank full of water has the following shape: Hemisphere - 5 m radius. at the bottom Cylinder - radius 5 m and height 10m in the middle Circular cone radius 5 m and height 4 m at the top The top of the tank is 2 m

asked by Amy on November 10, 2010
5. ### Calculus 2

An underground tank full of water has the following shape: Hemisphere - 5 m radius. at the bottom Cylinder - radius 5 m and height 10m in the middle Circular cone radius 5 m and height 4 m at the top The top of the tank is 2 m

asked by Amy on November 10, 2010
6. ### Physics

Assume you construct a new water tower for a town water supply. Assume the tank is in the shape of a sphere with a diameter of 21ft. Assume the tank is made of formes and welded .5 in steel plate that weighs 150 lb per ft3. What

asked by Lindsey on July 9, 2012

More Similar Questions