Four horses are tied with equally long ropes at the four corners of a square field whose side is $140$ metre such that they can graze maximum grass without entering the field of one another. Calculate the area of the grass which cannot be grazed by them.

Open in App

Solution

The length of the ropes should be 70 m.
$∴$ Area of the grass (which cannot be grazed)
= Area of ABCD - Area of the circle (radius = 70 m)
$= (140)^{2} - π (70)^{2}$
$= 140^{2} - \frac{22}{7} \times 70 \times 70$
$= 19600 - 15400$
$= 4200$ sq. m.

Suggest Corrections

Similar questions

Q. A horse is tied to a pole fixed at one corner of a

30 m \times 30 m

square field of grass, by means of a

10 m

long rope. Find the area of the field, in which the horse can graze? (Take

π = 3.14

)

Q. A horse is tied with a rope of length

28

metre. Calculate the grass which can be grazed by the horse.

A horse is tied to a peg at one corner of a square shaped grass field of side $15 m$ by means of a $5 m$ long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were $10 m$ long instead of $5 m$ . (Use $π = 3.14$ )

Q. A horse is tied to a pole fixed at one corner of a

50 m \times 50 m

square field of grass by means of a

20 m

long rope. What is the area to the nearest whole number of that part of the field which the horse can graze?

Q. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig below). Find the area of that part of the field in which the horse can graze.

Join BYJU'S Learning Program

Four horses are tied with equally long ropes at the four corners of a square field whose side is 140 metre such that they can graze maximum grass without entering the field of one another. Calculate the area of the grass which cannot be grazed by them.

The length of the ropes should be 70 m.∴ Area of the grass (which cannot be grazed)= Area of ABCD - Area of the circle (radius = 70 m)=(140)2−π(70)2=1402−227×70×70=19600−15400=4200 sq. m.

Four horses are tied with equally long ropes at the four corners of a square field whose side is $140$ metre such that they can graze maximum grass without entering the field of one another. Calculate the area of the grass which cannot be grazed by them.

The length of the ropes should be 70 m.
$∴$ Area of the grass (which cannot be grazed)
= Area of ABCD - Area of the circle (radius = 70 m)
$= (140)^{2} - π (70)^{2}$
$= 140^{2} - \frac{22}{7} \times 70 \times 70$
$= 19600 - 15400$
$= 4200$ sq. m.