Question

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is

Answer 1

Solution -

Refer to the attached figure .

Here , the side of the field is 15 m .

But , the maximum length of the rope is 7 m .

So, thus forms a quarter circle .

Area of that quarter circle -

=> ( 90 / 360 ) π r ²

=> ( 1 / 4 ) × ( 22 / 7 ) × 7²

=> ( 77 / 2 )

=> 38 .5 m ^ 2 .

This is the required area of the field the horse can graze ...

Thus , that is the final answer .

___________________

Answer 2

Answer:

Question:-

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is ?

Answer:-

Given:-

side of square shaped grass field = 15 m

length of rope = 7 m

to find:-

The area of that part of the field in which the horse can graze

solution:-

Let ABCD be square field

And , length of rope = 7 m

hence (r) = 7m

we need to find area of feild which horse can graze,

ie, area of sector QBP

note - in square all sides are 90°

Hence , angle QBP = 90°

Area of sector QBP =>

$\frac{90}{360} \times {πr}^{2}$

$\frac{90}{360} \times3.14 \times {7}^{2}$

$\frac{1}{4} \times 3.14 \times 7 \times 7$

$\frac{3.14 \times 49}{4}$

$= 38.465$

Hence ,

Area of feild with horse can graze = Area of sector QBP

$= {38.465}^{2}$