Question

A horse is tied to a peg at one corner of square shaped grass field of side 15 m by means of 5 m long rope, find

1. The area of that part of the field in which the horse can graze. 
2. The increase in the grazing area if the rope were 10 m long instead of 5 m. (π = 3.14)

Answer 1

Given:

Side of the square field = 15 m

Initial length of the rope (r₁) = 5 m

Increased length of the rope (r₂) = 10 m

Angle of the sector (θ) = 90°

Value of π = 3.14

a. The area of that part of the field in which the horse can graze:

Area grazed = `1/4 xx π xx r_1^2`

= `1/4 xx 3.14 xx 5 xx 5`

= `78.5/4`

= 19.625 m²

b. The increase in the grazing area if the rope were 10 m long instead of 5 m:

Area grazed = `1/4 xx π xx r_2^2`

= `1/4 xx 3.14 xx 10 xx 10`

= `314/4`

= 78.5 m²

Now, find the increase in area:

Increase = 78.5 – 19.625

= 58.875 m²