# 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 areas of sector of circles and areas of squares 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 angle with degree measure 90° (as the peg is at the corner of a square and

The angle of square = 90° and length of the rope = 5 m)

Area of the field horse can graze = Area of the sector

= θ/360° × πr^{2}

= 90°/360° × πr^{2}

= 1/4 πr^{2}

(ii) Similar to the first part

The area that can be grazed by the horse when the length of the rope is 10m, is an area of a sector of a circle with a radius (r ) 10 m and an angle with a degree measure 90°

Area of the field horse can graze = Area of the sector

= 90°/360° × πr_{1}^{2}

= 1/4 πr_{1}^{2}

Increase in the grazing area

= 1/4 πr_{1}^{2} - 1/4 πr^{2}

= 1/4 π (r_{1}^{2} - r^{2})

(i) Area of the field the horse can graze = Area of a sector of in a circle of radius 5 m

= 90°/360° × π × (5 m)^{2}

= 25/4 × 3.14 m^{2}

= 19.625 m^{2}

(ii) Area that can be grazed by the horse when the rope is 10 m long = 90°/360° × π × (10 m)^{2}

= 1/4 × 3.14 × 100 m^{2}

= 78.5 m^{2}

Increase in grazing area = 78.5 m^{2} - 19.625 m^{2} = 58.875 m^{2}

**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:

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)

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 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 are 19.625 m^{2} and 58.875 m^{2} respectively.