I did it the following way:

if you draw a circle around a corner of the square with radius of 10, the part which covers the circle and square would be exactly 1/4 of a circle.

i) Area of the sector = (pi*r^2)(angle of the sector)/360

(100*pi)(90/360) = 25pi


now r = 20

ii) Area of the sector = (400*pi)(90/360) = 100pi

Therefore the increase in grazing is 100pi - 25pi = 75pi

It can be a little hard to visualize this without a diagram. Hope the answers are right. Do these answers match the OA?

Yea, those answers are right. I think the question attempts to throw the test-taker off by giving the information that the field is 30 by 30. This information is only necessary to show that the field is a square and that the rope is not longer than the field.

Since it is a square, simply find the area of the circle with r = 10 and r =20 and divide them by 4.