Question

The radius of the circle is increasing at a rate of 2 meters per minute and the sides of the square are increasing at a rate of 1 meter per minute. When the radius is 6 meters, and the sides are 24 meters, then how fast is the AREA outside the circle but inside the square changing?

Answer 1

Change in area=24
`\pi`-48

Explanation:

Let s will be the side of square and r will be the radius of circle.

Then two given conditions are

1)dr/dt=2 m/s

2)ds/dt=1 m/s

Area enclosed=(Area of square)-(Area of circle)

Area of square=
`s^(2)`

Area of circle=
`\pi r^(2)`

Area enclosed=
`(\pi r^(2))-s^(2)`

dA/dt=2
`\pi`r(dr/dt)-2s(ds/dt)

At s=24,and r=6

dA/dt=2(
`\pi`)(6)(2)-2(24)(1)

Change in area=24
`\pi`-48