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read pi

by sanju09 » Sat Feb 20, 2010 2:41 am
In a square of side 10, four semicircles are drawn in the interior of the square region, by taking each side of the square as diameter. If π (read pi) is 3.14, then what is the area of the region obtained by the intersections of the four semicircles?
(A) 51
(B) 54
(C) 57
(D) 60
(E) 63
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by ajith » Sat Feb 20, 2010 3:04 am
sanju09 wrote:In a square of side 10, four semicircles are drawn in the interior of the square region, by taking each side of the square as diameter. If π (read pi) is 3.14, then what is the area of the region obtained by the intersections of the four semicircles?
(A) 51
(B) 54
(C) 57
(D) 60
(E) 63
Area of intersection = 4* area of semi circle - area of the square
= 157- 100 = 57
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by sanju09 » Sat Feb 20, 2010 3:33 am
ajith wrote:
sanju09 wrote:In a square of side 10, four semicircles are drawn in the interior of the square region, by taking each side of the square as diameter. If π (read pi) is 3.14, then what is the area of the region obtained by the intersections of the four semicircles?
(A) 51
(B) 54
(C) 57
(D) 60
(E) 63
Area of intersection = 4* area of semi circle - area of the square
= 157- 100 = 57
KILLLLER! So direct, didn't care to explain segment's area [spoiler]OA C[/spoiler]
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by shashank.ism » Sat Feb 20, 2010 8:26 am
sanju09 wrote:
ajith wrote:
sanju09 wrote:In a square of side 10, four semicircles are drawn in the interior of the square region, by taking each side of the square as diameter. If π (read pi) is 3.14, then what is the area of the region obtained by the intersections of the four semicircles?
(A) 51
(B) 54
(C) 57
(D) 60
(E) 63
Area of intersection = 4* area of semi circle - area of the square
= 157- 100 = 57
KILLLLER! So direct, didn't care to explain segment's area [spoiler]OA C[/spoiler]
when u will dra the diagram and will analyse, area of four semi-circles - area of square
you will find that area of four semicircles includes area of the req intersection twice + area of not required section
and when u subtract area of square u actually subtract area of the req intersection (once) + area of not required section(once)

so u get the required value
hence Area of intersection = 4xarea of semi circle - area of the square
= 4 x (3.14 x 5^2)/2-100 = 57 Ans C
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by thephoenix » Sat Feb 20, 2010 8:52 am
FROM DIAGRAM ITS VISIBLE THAT REQD AREA= 4* AREA OF SEMICIRCLES -AREA OF SQ=157-100=57
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