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Volume of a Cone: 21

3r hπ Volume of a Cylinder:

2r hπ Volume of a Sphere:

34

3rπ

1.) The base of a triangle is increasing at a rate of 2 inches per minute. If the height is

always 3 times the base, how fast is the area changing when the base is 6 inches?

2.) A cubical block of ice is melting so that it is losing 3 cubic inches/min. How fast is each

side changing when the block is 40 inches on a side?

3.) Oil from an uncapped well off the coast of Louisiana is radiating outward in the form of a

circular film on the surface of the water. If the radius is increasing at the rate of 2meters

per minute, how fast is the area of the oil film growing when the radius reaches 100

meters

4.) A cylindrical tank with a radius of 6 meters is filling with fluid at a rate of 108π cubic

meters per second. How fast is the height increasing

5.) A 20 foot ladder is leaning against a wall and sliding toward the floor. The rate at which

the base of the ladder is sliding away from the wall is 10 feet per second. How fast is the

ladder sliding towards the ground when the top of the ladder is 12 feet from the ground?

6.) The rate of change of the radius of a cone is 2 inches per minute. If the height of the

cone is always 3 times the radius, find the rate of change of the volume of the cone when

the radius is 6 inches

7.) A rocket rising vertically at 5400 mph. An observer on the ground is standing 20 miles

from the launch pad. How fast (in radians per second) is the angle of elevation changing

where the rocket is 40 miles from the ground.