A stable owner has four horses. He usually tie these horses . . .

Question : A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But trying with rope sometimes result in injuries to his horses, so he decided to built fence around the area so that each horse can graze. 

Based on the above, answer the following questions : 

(i) Find the area of the square shaped grass field. [1 Mark]

(ii) 
(a) Find the area of the total field in which these horses can graze. [2 Marks]
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m, find the area grazed by one horse. [Use π=3.14] [2 Marks]

(iii) What is the area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm. [1 Marks]

CBSE Outside Delhi [2024] (30/3/1)

Solution : 

This is a case study based question from Area Related to circles (Mensuration).

Here side of the square (a) = 20 m

Length of the rope (r) = 7 m

(i) Find the area of the square shaped grass field. 

Ans : 

Area of square shaped grass field 
= (side)²
= a²
= (20)²
= 400 m²

(ii) 

(a) Find the area of the total field in which these horses can graze.

Ans : 

Required Area
=4×Area of sector
=4×[θ/360]×[π](r)²
=4×[90/360]×[22/7](7)²
=4×[1/4]×22×7
=22×7
=154 m²

OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m, find the area grazed by one horse. [Use π=3.14]

Ans : 

Here,
New Radius (r') =10 m

Area grazed by one horse when the rope is increased from 7 m to 10 m 

= [θ/360]×[π](r)²

= [90/360]×[3.14](10)²
= [1/4]×314
= 78.5 m²

(iii) What is the area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm. 
Ans : 

Area of the field left ungrazed 
= Area of field - area of field grazed by 4 horses
= 400 m² - 154 m²
= 246 m²