Question

At one corner of a square shape field of sife 25 m a cow is tied by 14 long rope what is the area of the part of the field in which cow can graze

Answer 1

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Answer 2

Given,

A square-shaped field of 25m sides.

A cow is tied with a rope of a length of 14 m at one corner of the square field.

To Find,

The area inside the square, where the cow can graze.

Solution,

The attachment shows a square field ABCD and the shaded part is the area in which the cow can graze, that is APQ.

As it can be seen that APQ is one-fourth part of the circle with A as its center.

Now since the length of the rope tied to the cow = $14$ m

⇒ The radius of the shaded area = $14$ m

Area of the circle = π$r^{2}$

Thus the area of the circle in the diagram = π×$14^{2}$ = $\frac{22}{7}$×$14$×$14$ = $616$

Now since only one-fourth part of the circle can be grazed by the cow,

⇒ $\frac{Total area of circle}{4}$ = $\frac{616}{4}$ = $154$

Henceforth, the area of the field, the cow can graze is 154 sqmtrs.