Question

a cow is tied with a rope to one corner of a square field of side 50m. If the length of the rope is 14m, find the area the cow cannot graze.

Answer 1

I have solved if the cow is tied at all four corners

Answer 2

The area that the cow cannot graze is 2346 m².

Given data :

Square field's side = 50m

Length of the rope = 14m

Now,the cow is tied in one corner of the field. And we know that a square's corner = 90°.

90° = 360°/4 = 1/4th of a circle.

So,the arc created in the corner of a square,by taking the corner point as the centre,then the formed area will be 1/4th of the circle.

And,here the length of the rope will act as the radius of that 1/4th circle.

So,the area will be = [{π×(14)²}÷4] = ( 616÷4) = 154 m²

Field's total area = (50×50) = 2500m²

So,the area which cannot be grazed by the cow =(2500-154) = 2346 m² (ans)