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If a wire is bent into the shape of a square, then the area enclosed

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If a wire is bent into the shape of a square, then the area enclosed  [#permalink]

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New post Updated on: 25 Sep 2017, 03:06
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If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. When the same wire is bent into semi-circle. then the area of semi circle will be

A. 22 cm square
B . 44 cm square
C. 77 cm square
D. 81 cm square
E. 154 cm square

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Originally posted by nkmungila on 25 Sep 2017, 02:46.
Last edited by pushpitkc on 25 Sep 2017, 03:06, edited 1 time in total.
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Re: If a wire is bent into the shape of a square, then the area enclosed  [#permalink]

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New post 25 Sep 2017, 03:05
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If the wire is bent into the shape of a square and the area is 81 \(cm^2\)
the side of the square is 9 cm. Hence, the perimeter is 4*side = 36 cm

This wire is not bent to form a semicircle which can be given by pi*r + 2*r(where r is the radius of the semicircle)

r(pi + 2) = 36 where pi = \(\frac{22}{7}\)

Therefore, r (\(\frac{36}{7}\)) = 36 => r = 7

The area of the semicircle is \(\frac{1}{2}*pi*r^2 = \frac{1}{2}*\frac{22}{7}*7*7 = 77 cm^2\)(Option C)

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Re: If a wire is bent into the shape of a square, then the area enclosed &nbs [#permalink] 25 Sep 2017, 03:05
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