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HCU MCA 2013 Paper

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Question : 4 of 75

Marks: +1, -0

Four cows are tethered at four corners of a square plot of side 14 m, so that the adjacent cows can just reach one another. There is a small circular pond of area 20 m

^2

at the centre. The area left ungrazed is

22 m $^2$
42 m $^2$
84 m $^2$
168 m $^2$

Solution:

(a) Area of sector at one corner

=\frac{\pi(7)^2}{4}

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{22}{7}\times\frac{7^2}{4}

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\frac{154}{4}

∴ Area of 4 sector =

\frac{154}{4}\times4=154

But area of given circular pond = 20 m

^2

∴Required ungrazed area

= Area of square - Area of 4 sector- Area of circular pond

=

(14)^2 - 154 - 20

= 196 -174

= 22 m

^2

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