Astone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s. (a) how rapidly is the area enclosed by the ripple increasing when the radius is 4 feet? the area is increasing at ft2/sft2/s. (b) how rapidly is the area enclosed by the ripple increasing at the end of 9 seconds? the area is increasing at ft2/sft2/s.

a. The area enclosed by the circular ripple is increasing at  when the radius is 4 feet.

b. The area enclosed by the circular ripple is increasing at  at the end of 9 seconds.

Given the following data:

a. To find how rapidly the area enclosed by the circular ripple is increasing when the radius is 4 feet:

Mathematically, we know that the area of a circle is given by the formula;

Where:

Next, we would differentiate with respect to time;

Substituting the values, we have;

× ×  ×

Therefore, the area enclosed by the circular ripple is increasing at  when the radius is 4 feet.

b.  To find how rapidly the area enclosed by the circular ripple is increasing at the end of 9 seconds:

First of all, we would determine the radius after 9 seconds as follows;

Radius, r = 21.6 feet.

Now, we can determine the rate at which the area is increasing:

Substituting the values, we have;

× ×  ×

Therefore, the area enclosed by the circular ripple is increasing at  at the end of 9 seconds.

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true tan speed = ang vel x radius