Question

Four cows are tethered at four corners of a square plot of side 21 meters such that the adjacent cows can just reach one another. There is a small circular pond of area 45sq.m at the centre. Then the area left ungrazed is.,

• A. 49.5 sqm
• B. 50 sqm
• C. 48 sqm
• D. 52.8 sqm

Answer 1

Answer:

A. 49.5 sqm

Side of Square = 21 meter

then the Length of rope $= \frac{21}{2}m$

Circular pond Area =45 m²

Area of square $=a^2=21\times{21}=441m^2$

Area of grazing /Area of Sector$=\frac{\theta}{360^o}\times{\pi{r^2}}$

$\theta$=angle of an sector which is $90^o\times{4}=360^o$

Area of grazing $=\frac{360^o}{360^o}\times{\frac{22}{7}\times{\frac{21}{2}\times{\frac{21}{2}}}}$

$=\frac{693}{2}=346.5sqm$

Then the area left ungrazed is., =Area of square - Area of grazing - area of pond

$=414-346.5-45$

$=49.5m^2$