Question

In a rectangular field which measures 15 m × 8m, cows are tied with a rope of length 3 m at four corners of the field and also at the centre. Find the area of the field where none of the cow can graze. (π = 3.14)

Answer 1

Area of the field where none of the cow can graze = Area of the rectangle – [Area of 4 quadrant circles] – Area of a circle

Area of the rectangle = l × b units²

= 15 × 8 m² = 120 m² 

Area of 4 quadrant circles = `4 xx 1/4 pi"r"^2  "units"`

Radius ofthe circle = 3 m

Area of 4 quadrant circles = `4 xx 1/4 xx 3.14 xx 3 xx 3`  = 28.26 m² 

Area of the circle at the middle = πr² units

= 3.14 × 3 × 3m² = 28.26m²

∴ Area where none of the cows can graze

= [120 – 28.26 – 28.26] m² 

= 120 – 56.52 m² 

= 63.48 m²