Question

(1 point) A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.1 ft/s. (a) How rapidly is the area enclosed by the ripple increasing when the radius is 4 feet

Answer 1

Answer:

The area enclosed by the ripple increasing is 77.9 ft²/s.

Explanation:

Given that,

Radius increases at a constant rate = 3.1 ft/s

We need to calculate the area of circle

Using formula of area

$A=\pi r^2$...(I)

On differentiate equation (I) with respect to time

$\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}$

Where, r = radius

Put the value into the formula

$\dfrac{dA}{dt}=2\pi\times4\times3.1$

$\dfrac{dA}{dt}=77.9\ ft^2/s$

Hence, The area enclosed by the ripple increasing is 77.9 ft²/s.