Question

In a rectangular field which measures 15m×8m , cow's are tied with a rope of length 3m at four corners of the field and also at the centre. Find the area of the field where none of the cow can graze?

Answer 1

see figure, here it is clearly shown the area of the field where none of the cow can gaze.

so, area of the field where none of the cow can gaze = area of rectangular field - [4 × (1/4 area of circular field of radius 3m) + area of circular field of radius 3m]

= area of rectangular field - [2 × area of circular field of radius 3m]

= length × width - 2 × π( radius)²

= 15m × 8m - 2 π (3m)²

= 120 m² - 18π m²

= 120 m² - 56.52 m²

= 63.48 m²

hence area of the field where none of the cow can gaze = 63.48 m²

Answer 2

Consider 3m rope as radius as cows can move in thay circle. The total circles are 4 and each covers 1/4th the area of complete circle. Hence 1/4*4