A circle is inside a square. The radius of the circle is increasing at a rate of 5 meters per day and the sides of the square are increasing at a rate of 4 meters per day. When the radius is 3 meters, and the sides are 21 meters, then how fast is the AREA outside the circle but inside the square changing

Area of the portion outside the circle but inside the square is reduced by 114 m² after the third day, reduced by  239.14284 in the fourth day.

Step-by-step explanation:

First day

Radius of the circle = 3 meters

Length of sides of the square = 21 meters

Area of the circle = π R2   = 22/7 x 32  = 28.285714 m²

Area of the square = L x B = 21 x 21 = 441 m²

Area of area outside the circle but inside the square = 412.71429 m²

Second day

Radius of the circle = 8 meters

Length of sides of the square = 25 meters

Area of the circle = π R2   = 22/7 x 82  = 201.14286 m²  

Area of the square = L x B = 25 x 25 = 625 m²

Area of area outside the circle but inside the square = 423.85714 m²

Third day

Radius of the circle =13 meters

Length of sides of the square = 29 meters

Area of the circle = π R2   = 22/7 x 132  = 531.14286 m²

Area of the square = L x B = 29 x 29 = 841 m²

Area of area outside the circle but inside the square = 309.85714 m²

Fourth day

Radius of the circle =18 meters

Length of sides of the square = 33 meters

Area of the circle = π R²   = 22/7 x 182  =1018.2857 m²  

Area of the square = L x B = 33 x 33 = 1089 m²

Area of area outside the circle but inside the square = 70.7143 m²

From the second and third day, it can be noticed that the area of the portion outside the circle but inside the square is reducing changing by half.