Question

Four cows are tethered at four corners of a Rectangular plot of size 30x20 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. 208.5
• B. 310
• C. 220
• D. 146

Answer 1

Answer:

A. 208.5

Length of rectangle = 30m

Breadth of rectangle = 20m

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

Circular pond Area =45 m²

Area of Rectangle $=L\times{B}=30\times{20}=600m^2$

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

$=600-346.5-45$

$=208.5m^2$