There is a circular pond in the middle of a square field and

There is a circular pond in the middle of a square field, and the area outside of the pond is 3300 square pu. The pond is 20 pu from the edge of the field. Find the side of the field and the diameter of the pond.

Solution

Let

area of circular pond =pie* r^2

area of square field= 4*a^2

As pond is 20pu from edge of field

we can say-> 2*(r+20) = a (side of square field)

also, 3300 =4*a^2 - pie* r^2

3300 = 4*4*(r+20)^2 -pie*r^2

solving this gives a quadratic equation in r.

(16-pie)r^2 + 640r +3100=0

r=5.44 or 44.34

a= 50.88 or 128.68