Question

Four horses are tethered at four corners of a square plot of side $63$ metres so that they just cannot reach one another. The area left ungrazed is :

• A. $675.5m^2$
• B. $780.6m^2$
• C. $785.5m^2$
• D. $850.5m^2$

Answer 1

The correct option is D $850.5m^2$

The length of the rope in which the horses tied should be equal to half of the side of the

square plot so that they just cannot reach one another.

$\therefore$, the length of the rope is $=\frac{63}{2}=31.5m$

The area covered by each horse should be equal to the area of sector with radius of $=\frac{63}{2}=31.5m$(length of the rope).

Total area covered by the four horses $=4\times$ area of sector of radius $31.5$ metres

$=$Area of circle of radius $31.5m.$

Area left grazed by the horses $=$ Area of square field $-$ Area covered by four horses.

$=632-\frac{22}{7}\times 31.5\times 31.5=3969-3118.5=850.5sq.m$