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(A) Let $ABCD$ be a rectangular field of dimensions $20 \, m 	imes 16 \, m$.Suppose,a cow is tied at a corner $A$. Let the length of the rope be $r =

Vedclass · Accepted Answer

$154$

Vedclass · Answer

(A) Let $ABCD$ be a rectangular field of dimensions $20 \, m 	imes 16 \, m$.Suppose,a cow is tied at a corner $A$. Let the length of the rope be $r = 14 \, m$.The area that the cow can graze is a sector of a circle with radius $r = 14 \, m$ and central angle $	heta = 90^{\circ}$ (since the corner of a rectangle is $90^{\circ}$).Area of the sector $= \frac{	heta}{360^{\circ}} 	imes \pi r^2$$= \frac{90^{\circ}}{360^{\circ}} 	imes \frac{22}{7} 	imes (14)^2$$= \frac{1}{4} 	imes \frac{22}{7} 	imes 196$$= \frac{1}{4} 	imes 22 	imes 28$$= 22 	imes 7 = 154 \, m^2$.

$A$ cow is tied with a rope of length $14 \, m$ at the corner of a rectangular field of dimensions $20 \, m \times 16 \, m$. Find the area of the field in which the cow can graze. (in $m^2$)

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