Posted by **EA** on Friday, March 28, 2014 at 11:39pm.

Jesse has constructed a huge cylindrical can with a diameter of 60 ft. The can is being filled with water at a rate of 450 ft3/min. How fast is the depth of the water increasing? (Hint: The volume of water in the cylinder is determined by πr2h where r is the radius and h is the depth of the water )

- Calculus -
**Damon**, Friday, March 28, 2014 at 11:48pm
the rate of change of volume is the surface area times the rate of change of height

450 ft^3/min = surface area * dh/dt

surface area = pi r^2

450 = pi (30^2) dh/dt

dh/dt = .159 ft/min

You could do this by saying

V = pi r^2 h

dV/dh = pi r^2

dV/dh*dh/dt = pi r^2 dh/dt

chain rule

dV/dt = pi r^2 dh/dt

but most of us just look at the lake rising an inch and seeing that the added volume is the area times one inch

- Calculus -
**EA**, Sunday, March 30, 2014 at 10:17pm
Thanks Damon, that really clears it up for me

## Answer This Question

## Related Questions

- calculus - A 24ft high conical water tank has its vertex on the ground and ...
- calculus - A trough is 16 ft long and its ends have the shape of isosceles ...
- Calculus - An inverted conical tank is being filled with water, but it is ...
- calculus - water is being siphoned from a cylindrical tank of radius 10m into a ...
- intro to calc - if the pool is being filled at a rate of .8ft^3/min, how fast is...
- calculus - A trough is 15 ft long and its ends have the shape of isosceles ...
- Calculus - A water trough is 9 m long and has a cross-section in the shape of an...
- Calculus Help Please!!! - A water trough is 5 m long and has a cross-section in ...
- calculus - A rectangular prismatic tank has the following dimensions :length is...
- Calculus - A rectangular prismatic tank has the following dimensions :length is...

More Related Questions