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A cow is tied with a rope of length \[14\] m at the corner of a rectangular field of dimensions \[20m\times 16m\]. Find the area of the field in which the cow can graze.
A cow is tied with a rope of length \[14\] m at the corner of a rectangular field of dimensions \[20m\times 16m\]. Find the area of the field in which the cow can graze.
Areas Related to Circles | Exercise 11.3 | Maths | NCERT Exemplar
A cow is tied with a rope of length \[14\] m at the corner of a rectangular field of dimensions \[20m\times 16m\]. Find the area of the field in which the cow can graze.

Let us consider ABCD be a rectangular field.

Given, Length of the field = \[20\] m

Given, Breadth of the field = \[16\] m

From the given question,

A cow is tied with a rope at a point A.

Let us consider length of rope be AE = \[14\] m = l.

We know that Angle subtended at the centre of the sector = \[{{90}^{\circ }}\]

Now for Angle subtended at the center (in radians) \[\theta \] = \[90\pi /180\] = \[\pi /2\]

∴ Area of a sector of a circle = \[\frac{1}{2}{{r}^{2}}\theta \]

= \[\frac{1}{2}\times {{(14)}^{2}}\times (\pi /2)\]

=  \[154\] \[{{m}^{2}}\]

Therefore, the area of the field in which cow can graze is \[154\] \[{{m}^{2}}\]

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