Question

a horse is tethered to one corner of a square plot of side 42 m by a rope 30m long rope then find area that it graze and also find the area that is left ungrazed ​

Answer 1

Answer:

The area which the horse can graze = 706.5  m²

The area that is left ungrazed ​= 1057.5  m²

Step-by-step explanation:

When a horse is tethered to one corner of a square plot , it can graze the area in form of a quadrant of a circle .

So, the area which the horse can graze = 1/4 * pi * r * r

where,  r  =  length of rope = 30 m

=>  the area which the horse can graze = 1/4 * 3.14 * 30 * 30

                                                          =   706.5  m²

So, the ungrazed area is the leftover area .

=> the area that is left ungrazed ​ = area of square plot - area grazed by horse

   So , the area of square plot  =  side * side

                                             =  42 * 42

                                             =    1764  m²

=>  the area that is left ungrazed ​ =  1764 - 706.5

                                                    =   1057.5  m²

Answer 2

Answer:

Grazed Area = 706.5 m²

Ungrazed Area = 1057.5 m²

Step-by-step explanation:

a horse is tethered to one corner of a square plot of side 42 m by a rope 30m long rope then find area that it graze and also find the area that is left ungrazed

Square plot side = 42 m

Plot Area  = 42 * 42 = 1764 m²

Horse is tied at one corner with 30 m  rope so he will  graze in circular shape with 90 deg segment as in square sides are at right angle

Area of segment grazed =  $(\frac{90}{360}) \pi R^2$

R = 30 m $\pi = 3.14$

= $(\frac{1}{4})\times 3.14 \times 30^2\\\\= 0.785 \times 900\\\\= 706.5 m^2$

Grazed Area = 706.5 m²

Ungrazed Area = Total Area - Grazed Area

=>Ungrazed Area = 1764 - 706.5

=> Ungrazed Area = 1057.5 m²