Math, asked by aryannp08, 3 months ago

A cow is tied up for grazing inside a rectangular field of dimensions 70 m ×50 m, in one corner of the field
by a rope of length 21 m. Find the area of the field on which the cow could not graze. Also find the perimeter
of the part of the field in which the cow could not graze. (π = 22

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Answers

Answered by mathdude500
3

Given :-

  • A rectangular field of dimensions 70 m × 50 m.

  • A cow is tied in one corner by a rope of length 21 m.

To Find :-

  • The area of the field on which the cow could not graze.

  • The perimeter of the field on which the cow could not graze.

Formula Used :-

 1. \:  \:  \: \boxed{ \tt{Area_{(quadrant)} = \dfrac{1}{4} \: \pi \:  {r}^{2}  }}

2. \:  \:  \boxed{ \tt{Area_{(rectangle)} = Length \times Breadth}}

\large\underline{\bold{Solution-}}

Given that,

Dimensions of field are

Length = 70 m

Breadth = 50 m

 \sf \: Area_{(rectangular \: field)} = Length \times Breadth

 \sf \: Area_{(rectangular \: field)} = 70 \times 50

\sf \: Area_{(rectangular \: field)} =3500 \:  {m}^{2}

Now,

Cow is tied at one corner by a rope of 21 m.

So,

Radius, r = 21 m

Hence,

Area of field grazed by cow is

 \sf \: Area_{(cow \: grazed)} = \dfrac{1}{4} \pi \:  {r}^{2}

 \sf \: Area_{(cow \: grazed)} = \dfrac{1}{4}  \times \dfrac{22}{7}  \times 21 \times 21

 \sf \: Area_{(cow \: grazed)} = 346.5 \:  {m}^{2}

Hence,

Area of field not grazed by cow is given by

 \bf \: Remaining  \: Area = \sf \: Area_{(rectangular \: field)}  -  Area_{(cow \: grazed)} =

 \sf \: Remaining  \: Area = 3500 - 346.5

 \therefore \: \sf \:  Remaining  \: Area  \: =  \: 3153.50 \:  {m}^{2}

Now, we have to find the Perimeter of field not grazed by cow,

So,

Required Perimeter is

 =  \sf \: (70 - 21) + (50 - 21) + \dfrac{1}{4} (2\pi \: r)

 =  \:  \sf \: 49 + 29 + \dfrac{1}{2}  \times \dfrac{22}{7}  \times 21

 =  \:  \sf \: 78 + 33

 =  \:  \sf \: 111 \: m

Additional Information :-

 \boxed{ \tt{Area_{(circle)} = \pi \:  {r}^{2} }}

 \boxed{ \tt{Area_{(sector)} = \dfrac{\pi \:  {r}^{2} \theta }{360} }}

 \boxed{ \tt{Area_{(square)} =  {(side)}^{2} }}

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