Hello, SuperTyphoon!

5. A circle is inscribed in a square. The circumference of the circle is increasing at a constant

rate of 6 in/sec. As the circle expands, the square expands to maintain tangency.

A. Find the rate at which the perimeter of the square is increasing. Code:

*-------*-*-*-------*
| * * |
| * * |
|* *|
| |
* *
2r * * - - - - *
* r *
| |
|* *|
| * * |
| * * |
*-------*-*-*-------*
2r

The radius of the circle is

The side of the square is

The circumference of the circle is: .

Differentiate with respect to time: .

We are told that

So we have: . in/sec. .[1]

The perimeter of the square is: .

Differentiate with respect to time: . .[2]

Substitute [1] into [2]: .

B. When the area of the circle is 25π inē,

find the rate on increase of the area between the circle and the square.

The area of the circle is: .

If the area is inē, we have: . .[3]

The area of the square is: .

The difference of the areas is: .

Differentiate with respect to time: . .[4]

Substitute [1] and [3] into [4]: .