Question

a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 6.4 seconds?

Answer 1

In 139.4 $\pi$ $ft^2$sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

What is area of circle?

 For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. We can determine the boundary length, or the circle's circumference, using the area formula.

Here area of circle

=> A= π$r^2$--------> 1

Differentiating 1 with respect to to time then

=> $\frac{dA}{dt}= 2\pi r\frac{dr}{dt}$

If the radius is  increasing at a constant rate 3.3ft/sec then after 6.4 seconds, radius is

=> 6.4*3.3=21.12 ft.

We know $\frac{dr}{dt}= \frac{3.3ft}{sec}$ and so ,

=> $\frac{dA}{dt}$ = 2*$\pi$*21.12*3.3=139.4 $\pi$ $ft^2$sec.

Hence In 139.4 $\pi$ $ft^2$sec rapidly is area of enclosed by the ripple increasing at the end of 6.4 seconds.

To learn more about area of circle refer the below link

brainly.com/question/10645610

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