- #1

Schaus

- 118

- 5

## Homework Statement

A stone is dropped into some water and a circle of radius r is formed and slowly expands. The perimeter of the circle is increasing at 3 m/s. At the moment the radius is exactly 2m, what rate is the radius of the circle increasing?

Answer ## \frac {dr} {dt} = 0.48 m/s##

## Homework Equations

## C = 2πr##

## A = πr^2##

## The Attempt at a Solution

## \frac {dC} {dt} = 3 m/s##

## \frac {dr} {dt} = ?##

## C = 2πr##

Taking the derivative of circumference formula

## \frac {dC} {dt} = 2π \frac {dr} {dt}##

Subbing in my ## \frac {dC} {dt} = 3 m/s##

## 3 = 2π \frac {dr} {dt}##

Dividiving both sides by 2π gives me 4.71 m/s. I have also tried doing this with the Area of a circle formula but I still got 2.36 m/s which is no where near the 0.48 it is supposed to be. Any help would be greatly appreciated.