A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find
(i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m.
(Use π = 3.14)
Solution:
We use the concept of area of a sector and area of a square to solve the problem.
(i) From the figure it’s clear that the horse can graze an area of a sector of a circle with radius (r) 5m and an angle with a degree measure 90° [Since its a square field]
Length of the rope = 5 m
Area of the field the horse can graze = Area of the sector with θ = 90° and r = 5
= θ/360° × πr2
= 90°/360° × πr2
= 1/4 × π × (5 m)2
= 25/4 × 3.14 m2
= 19.625 m2
(ii) The area that can be grazed by the horse when the length of the rope is 10m, is the area of the sector of a circle with a radius (r) 10 m and an angle with a degree measure 90°.
Area of the field the horse can graze = Area of the sector with θ = 90° and r = 10
= 90°/360° × πr2
= 1/4 × 3.14 × 100 m2
= 78.5 m2
Increase in the grazing area
= 78.5 m2 - 19.625 m2
= 58.875 m2
☛ Check: NCERT Solutions for Class 10 Maths Chapter 12
Video Solution:
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 12.11). Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.2 Question 8
Summary:
If a horse is tied to a peg at one corner of a square-shaped grass field of side 15 m by means of a 5 m long rope, the area of the field where the horse can graze and the increase in the grazing area if the rope were 10 m long instead of 5 m are 19.625 m2 and 58.875 m2 respectively.
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