Related Rates

Water slowly evaporates from a circular shaped puddle. The area of the puddle decreases at a rate of $$36\pi\ \frac{in^2}{hr}$$ . Assuming the puddle retains its circular shape, at what rate is the radius of the puddle changing when the radius is 5 in?

A hypothetical cube grows at a rate of  $$64\ \frac{m^3}{\min}$$ . How fast are the sides of the cube increasing when the sides are 8 m?

A spherical snowball is rolled in fresh snow, causing it to grow so that its radius increases at a rate of 2 in/sec. How fast is the volume of the snowball increasing when the radius is 2 in?

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 3 cm/min. How fast is the area of the pool increasing when the radius is 12 cm?

A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fast is the volume of the balloon increasing when the radius is 3cm?

$$V=\frac{4}{3}\pi r^3$$

A 10ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 6ft from the wall?

The length of a rectangle is increasing at a rate of 44 inches per second while its width is decreasing at a rate of 33 inches per second. At what rate, in square inches per second, is the area of the rectangle changing when its length is 23 inches and its width is 18 inches?

A 20-foot ladder leans against the wall of a building. The ladder starts sliding down the wall so that the top of the ladder moves down at the rate of 0.5 ft/sec. How fast is the foot of the ladder moving away from the wall when the foot of the ladder is 12 feet from the wall?

A cylindrical tank is being filled with water at a rate of 5 cubic meters per minute. If the tank has a height of 8 meters and a radius of 3 meters, how fast is the water level rising when the water is 4 meters deep?