Name:
Date:
Section:
5.2
Related Rates and Shapes
1. If the radius of a circle is increasing at a rate of 2 inches per second, how fast is the
area of the circle increasing when the radius is 3 inches?
2. If the circumference of a circle is decreasing at a rate of 5 centimeters per minute, at
what rate is the radius of the circle changing when the radius is 4 centimeters?
3. Oil is leaking out of a car and is making a circular spill on the pavement. If the area of
the spill is increasing at a rate of
feet per hour, at what rate is the radius of the
spill increasing when the spill has a radius of 6 feet?
4. If the circumference of a circle is increasing at a rate of
meters per second, when
the radius of the circle is 3 meters how fast is the area of the circle increasing?
5. If the sides of a square are decreasing at a rate of 4 inches per minute, how fast is the
area of the square changing when the sides are 2 inches long?
6. If the perimeter of a square is increasing at a rate of 9 feet per second, how fast are the
sides of the square growing when the sides are each 3 feet long?
7. If the sides of a cube are increasing at a rate of 2 miles per hour, when the sides are 3
miles long how fast is the volume of the cube increasing?
8. If a cube is expanding at a rate of 3 cubic centimeters per minute, how fast are the
sides increasing when the sides of the cube are 4 centimeters?
9. How fast is the surface area of a cube increasing when the sides are 10 feet long, if the
sides are increasing at one foot per minute?
10. If a spherical balloon is being inflated at a rate of
cubic feet per minute, how fast
is the radius of the balloon expanding when the radius of the balloon is 9 feet?
11. If the radius of a sphere is increasing at a rate of 3 inches per minute, how fast is the
volume of the sphere increasing when the radius of the sphere is 2 feet? (be careful
on this one)
12. If the sides of a cube are decreasing at a rate of 3 meters per second, how fast is the
surface area decreasing when the sides are 2 meters long?
13. If the radius of the earth is increasing at a rate of 5 miles per hour, how fast is the
surface area of the earth increasing when the radius of the earth is 500 miles?