Four horses are tethered at four corners of a square plot of side $14$ metres (m) so that the adjacent horses can just reach one another. There is a small circular pond of area $20 m^{2}$ at the centre. Find the ungrazed area?

18

sq. m

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20

sq. m

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22

sq. m

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24

sq. m

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Solution

The correct option is D $22$ sq. m
Since the horses just reach each other while grazing
So they will form a quadrant of circle of radius 7m

$∴$ Ungrazed area=Area of square-4( area grazed by one horse)-Area of pond
= $14^{2} - 4 (\frac{π (7)^{2}}{4}) - 20$

= $196 - 154 - 20$

= $22 s q . m e t e r$

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Four horses are tethered at four corners of a square plot of side 14 metres (m) so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area?

The correct option is D 22 sq. m Since the horses just reach each other while grazing So they will form a quadrant of circle of radius 7m∴ Ungrazed area=Area of square-4( area grazed by one horse)-Area of pond =142−4(π(7)24)−20 =196−154−20 =22sq.meter

Four horses are tethered at four corners of a square plot of side $14$ metres (m) so that the adjacent horses can just reach one another. There is a small circular pond of area $20 m^{2}$ at the centre. Find the ungrazed area?