1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what rate is the volume increasing when the radius is 5 inches?

2. A particle moves in a circular orbit x2 + y2 = 16. As it passes through the point (2, 2 3 ), its y-coordinate decreases at a rate of 3 units per second. At what rate is the x coordinate changing?

3. A point moves along the straight line x + 3y = 6. Find the rate of change of the y-coordinate, given that the x-coordinate is increasing at a rate of 3 units per second.

4. If a point is moving along y = 3x2 - 4x - 6 at a rate of dx dt = 4 m/s, find dy dt , when x = 3.

5. A heap of garbage in the shape of a cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters.

6. A circle with area A = is expanding with time. If 2 r dA dt = 5 cm2 /s, what is dr dt when r = 6?

7. A triangle, whose h = 2b, has an area A = 1 1 bh b(2b) 2 2 = = b2 is expanding with time. If dA dt = 8 cm2 /s, what is db dt when b = 2?

8. A sphere is expanding at the rate of 8 cm3 /sec, the formula for volume of a sphere is 4 3 V r 3 = , what is dr dt when r = 5?

9. A cone is expanding at the rate of 9 cm3 /sec, the formula for volume of a cone is: V = 2 r h 3 , let h = 2r, what is dr dt when r = 3?

10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm /s. What is the rate of change of the volume if r = 3 and V = r 2 h?