# math

posted by .

If the radius of a circular wave is increasing at 2 meters/sec, how fast is the area changing when the radius is 5 meters?

• math -

a = pi r^2
da/dt = 2pi r dr/dt
da/dt = 2pi * 5 * 2 = 20pi m^2/s

## Similar Questions

1. ### math

direct variation the surface area of a sphere varies directly as the square of the radius. if the surface area of a sphere is 36 pi meters squared when the radius is 3 meters, what is the surface area of a sphere with a radius of 6 …
2. ### math

The radius of a circular oil slick expands at a rate of 8 m/min. a. How fast is the area of the oil slick increasing when the radius is 30 m?
3. ### calculus

An athlete is running around a circular track of radius 50 meters at the rate of 5 meters per second. A spectator is 200 meters from the center of the track. How fast is the distance between the two changing when the runner is approaching …
4. ### CALC

The radius in meters of a circular oil slick increases at a rate of (12 - 0.3t), where t is measured in hours. Which of the following expressions would calculate the rate at which the area of the oil slick is increasing when the radius …
5. ### Calculus

The area of a floating circular oil spill in the ocean is increasing at a rate of 96pi square meters per second. When the area of the spill is 1000pi how fast is the radius increasing in meters per second.
6. ### calculus

The radius of the base of a right circular cylinder is r com and the height is 2r cm. Find the rate at which the surface area of the cylinder is increasing when the radius is 5 cm and the volume is increasing at 5pi cm/sec. Thank you!
7. ### Calculus

Let V be the volume of a right circular cone having height h and radius r and assume that h and r vary with time. a. Express the time rate of change of the cylinder in terms of h, r and their rates of change. b. At a certain instant, …
8. ### math

If the radius of a circular wave is increasing at 2 meters/sec, how fast is the area changing when the radius is 5 meters?
9. ### Calculus

A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/second while its height is increasing at the rate of 5 inches/second. When the radius is 4 inches and the height is 6 inches, how fast is …
10. ### Calculus

The radius of a conical tank is 2.7 meters and the height of the tank is 4.3 meters. Water is flowing into the tank at a constant rate of 59.5 m3/minute. At the instant the the depth of the water is 0.6 meters, answer the following: …

More Similar Questions