Water is falling on a surface, wetting a circular area that is expanding at a rate of 4 mm2 /s. How fast is the radius of the wetted area expanding when the radius is 150 mm

The radius of the wetter area expands at a rate of milimeters per second when radius is 150 milimeters.

Explanation:

From Geometry we remember that area of a circle is described by this expression:

(Eq. 1)

Where:

- Radius of the circle, measured in milimeters.

- Area of the circle, measured in square milimeters.

Then, the rate of change of the area in time is derived by concept of rate of change, that is:

(Eq. 2)

Where:

- Rate of change of radius in time, measured in milimeters per second.

- Rate of change of area in time, measured in square milimeters per second.

Now the rate of change of radius in time is cleared within equation above:

If we know that and , then the rate of change of radius in time is:

The radius of the wetter area expands at a rate of milimeters per second when radius is 150 milimeters.

the correct answer is b

the first, second, and fifth options