The radius of a sphere increases by cm per second. If is the volume of the sphere and is time measured in seconds, what is (in cm/s) for ?
The side length of a cube increases by cm per minute. If denotes the volume of the cube in , and denotes time measured in minutes, what is the change in volume over time (in ) for cm?
The radius of a sphere increases by cm per second. If denotes the surface area of the sphere, and denotes time measured in seconds, what is (in ) for ?
A spherical fish tank of radius 10 meters is being filled with at a constant rate of cubic meters of water per second. At height 6 meters, the rate of change of the height is 1 meter per second. What is the value of ?
Details and assumptions
The height is measured from the bottom of the sphere (i.e. in contact with the ground).
A circular conical reservoir, vertex down, has depth and top radius Water is leaking out at the rate of cubic feet per second. Find the rate at which the water level is dropping when the diameter of the surface is