PSP Calculus
Related Rate homework problems
Name _______________________________
1. A conical paper cup 3 inches across the top and 4 inches deep is full of water. The
cup springs a leak at the bottom and loses water at the rate of 2 cubic inches per
minute. How fast is the water level dripping at the instant when the water is exactly
3 inches deep? Express the answer in inches per minute. [Note: the formula for the
𝜋
volume of a cone of base radius r and height h is 𝑉 = 3 𝑟 2 ℎ]
2. Draining a reservoir: Water is flowing at the rate of 50 m3/min from a concrete
conical reservoir (vertex down) of base radius 45 m. and height 6 m. How fast is the
water level falling when the water is 5 m. deep? (a) Give your answer in m/min.
(b) Give your answer in cm/min.
3. Continuing with #2, give the rate at which the radius is changing when the water is
5 m. deep. (give your answer in both m/min and cm/min.)
4. Air is being pumped into a spherical balloon at the rate of 7 cubic centimeters per
second. What is the rate of change of the radius at the instant the volume equal 36π?
4𝜋
[The volume of a sphere is 𝑉 = 3 𝑟 3]
Name _______________________________
PSP Calculus
Related Rate homework problems
1. A conical paper cup 3 inches across the top and 4 inches deep is full of water. The
cup springs a leak at the bottom and loses water at the rate of 2 cubic inches per
minute. How fast is the water level dripping at the instant when the water is exactly
3 inches deep? Express the answer in inches per minute. [Note: the formula for the
𝜋
volume of a cone of base radius r and height h is 𝑉 = 3 𝑟 2 ℎ]
2. Draining a reservoir: Water is flowing at the rate of 50 m3/min from a concrete
conical reservoir (vertex down) of base radius 45 m. and height 6 m. How fast is the
water level falling when the water is 5 m. deep? (a) Give your answer in m/min.
3. (b) Give your answer in cm/min.
4. Continuing with #2, give the rate at which the radius is changing when the water is
5 m. deep. (give your answer in both m/min and cm/min.)
5. Air is being pumped into a spherical balloon at the rate of 7 cubic centimeters per
second. What is the rate of change of the radius at the instant the volume equal 36π?
4𝜋
[The volume of a sphere is 𝑉 = 3 𝑟 3]