Additional Related Rates Problems (Section 2.6)
1.
2.
As a balloon in the shape of a sphere is inflated, the radius is increasing at a rate of
1
inches per
π
second. At what rate is the volume of the balloon increasing when the radius is 1 inch?
− x2 + 4 x − 3
so that the y-value is decreasing at a rate of 3
10
units per second. Find the instantaneous rate of change of x with respect to time at the point on
the curve where x = 5 .
A particle moves on the curve y =
3.
A 5-meter long ladder is leaning against the side of a house. The foot of the ladder is pulled
away from the house at a rate of 0.4 meters per second. Determine how fast the top of the
ladder is moving down the side of the house when the foot of the ladder is 3 meters from the
house.
4.
The height of a cylinder with a radius of 4 centimeters is increasing at a rate of 2 centimeters per
minute. Find the rate of change in the volume of the cylinder with respect to time when the
height is 10 centimeters.
5.
The radius of a circle is increasing at the rate of 2 feet per minute. Find the rate at which the
area is increasing when the radius is 7 feet.
6.
A metal cube contracts when cooled. If the edge of the cube is decreasing a rate of 0.2
centimeters per hour, how fast is the volume changing when the edge is 60 centimeters?
7.
Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6
square miles per hour. How fast is the radius of the spill increasing when the area is 9 square
miles?
8.
A conical water tank with vertex down has a radius of 10 feet at the top and is 24 feet high. If
water flows into the tank at a rate of 20 cubic feet per minute, how fast is the depth of the
water increasing when the water is 16 feet deep?
9.
At 1200 hours, ship A is 150 kilometers west of ship B. Ship A is sailing east at 35 kilometers per
hour and ship B is sailing north at 25 kilometers per hour. How fast is the distance between the
ships changing at 1600 hours?
10.
A trough is 10 feet long and its ends have the shape of isosceles triangles that are 3 feet across
at the top with a height of 1 foot. If the trough is being filled with water at a rate of 12 cubic
feet per minute, how fast is the water level rising when the water is 6 inches deep?