Question

A goat is tied to a pole fixed at the
mid-point of the length of a rectangular
grassy field of dimensions 60 mx 30 m
by means of a 21 m long rope. Find the
area of the field that is grazed by the goat.​
Answer must be = 693m²​

Answer 1

$\text{Upon drawing the given scenario we get the following information:}$

$\text{The rope OP is 21 m long}$

$\text{The field is a rectangle ABCD, in which AB = 60 m and CD = 30m}$

$\text{We have to find the area of the field that is grazed by the goat}$

$\implies \text{We have to find the area of circle that is formed by OP}$

$\text{We know that Area of circle} = \pi r^{2} , \text{ where }r \text{ is the radius of circle}$

$\implies \text{Area of circle formed by OP} = \pi(21)^{2}$

$\text{We know that }\pi = \dfrac{22}{7}$

$\implies \text{Area of circle formed by OP} = \dfrac{22}{7}(21)(21)$

$\implies \text{Area of circle formed by OP} = (22)(3)(21)$

$\implies \text{Area of circle formed by OP} = 1386 \text{ m}^{2}$

$\therefore \boxed{\text{ The Area of field grazed by the goat is 1386 m}^{2}}$

Answer 2

Given :-

• Length of rectangular field = 60m
• Breadth of rectangular field = 30m
• Length of rope at the length of field = 21m

To Find :-

• Area grazed by the Goat = ?

Solutions :-

To calculate the area grazed by the Goat at first we have to notice in the given question. A goat is tied to a pole fixed at the mid-point of the length of a rectangular grassy field of dimensions 60 mx 30 m by means of a 21 m long rope. Here length of rope is the radius for circular region which is taken by the Goat during grazing in the rectangular field. It means area grazed by the Goat half of the circular region because the Goat is tied to a pole fixed at the mid point of length of the field.

=> Area of rectangular field = Length × Breadth

= 60 × 30

= 1800 m²

=> Area grazed by the goat = 1/2 of area of circular region

=> 1/2 × (π × r²)

=> 1/2 × (22/7 × 21 × 21)

=> 1/2 × (22 × 3 × 21)

=> 1/2 × 1386

=> 693 m²