Question

A calf is tied with a rope of length 6m at the corner of a square grassy lawn of side 20m. If the length of the rope is increased by 5.5m, find the increase in area of grassy lawn in whi the calf can graze.

Answer 1

Let the calf be tried at the corner A of the square lawn.Then, the increase in area = difference of two sectors of central angle 90 each and radii 11.5m (6m+5.5m) and 6m, which is shaded region in figure so,required increase in area = [90/360into pia into( 11.5)into 11.5-90/360into pia into6into ]msq
=75.625m.sq

Answer 2

Did you make a sketch?

The area reached by the horse is 1/4 of a circle with original radius of 6 m
that area = (1/4)π(36) = 9π m^2

after lengthening of rope, r = 11.5 m
new area for grazing = (1/4)π(11.5)^2 m^2
= 33.0625π m^2

So what is the increase in area ?

Answer 3

Thanx

Answer 4

No idea