Question

A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 3 feet per minute. Find the rate at which the area is changing at the instant the radius is 4 feet. When the radius is 4 ​feet, the area is changing at approximately nothing square feet per minute. ​(Type an integer or a decimal. Round to the nearest thousandth as​ needed.)

Answer 1

Rate of change of area is
`75.398ft^(2)/sec`

Step-by-step explanation:

`Area=\pi r^(2)\\\\(d(Area))/(dt)=(\pi r^(2))/(dt)=2\pi r(dr)/(dt)`

Applying values we get
`(d(Area))/(dt)=2\pi 4* 3=75.398ft^(2)/sec`