Problem Solving

A horse is tied to a pole fixed at one corner of a 30m x 30m square field of grass by means of a 10m long rope. (take pie value=3.14)

(i) Find the area of that part of the field in which the horse can graze
(ii) Find the increase in the grazing area if the rope were 20m long instead of being 10m long.

Thanks everyone.

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.