Acircle is inside a square. the radius of the circle is increasing at a rate of 4 meters per day and the sides of the square are increasing at a rate of 3 meters per day. when the radius is 3 meters, and the sides are 20 meters, then how fast is the area outside the circle but inside the square changing?

The area is changing by the rate of 44.62 meters per sec.

Step-by-step explanation:

Let x be the side of the square and r be the radius of the circle,

Then, the area outside the circle but inside the square is,

V = Area of square - area of circle,

∵ Area of a square = side² and area of a circle = (radius)²,

Thus,

Differentiating with respect to t ( time )

We have,

x = 20 meters, r = 3 meters,