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# 4965 PS > Geometry > Mixed Shapes How many

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4965 PS > Geometry > Mixed Shapes How many [#permalink]  05 May 2005, 00:21
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4965 PS > Geometry > Mixed Shapes

How many non-overlapping circles with circumference 4 can be drawn in a square with side 12?

(A) 81
(B) 36
(C) 12
(D) 9
(E) 3
Manager
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[#permalink]  05 May 2005, 02:50
the Answer is (A)=81
circumference=4 means 2*Pi*r=4
r=2/Pi => d=4/Pi The side of the square 12 with should by the diameter
to find how many circles can drawn
12/(4/Pi)=3*Pi=9.something
9 in each row 9 in every column 9*9=81
VP
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[#permalink]  05 May 2005, 13:21
D)...

circumference = diameter = 4 means 1 circle fits in square of area 16. area of square with side 12 is 144. 144/16=9=D)
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Manager
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[#permalink]  05 May 2005, 14:16
is it 4 or 4П? that makes a whole lot of difference.
Manager
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[#permalink]  05 May 2005, 22:28
I hope it'll be useful for you
http://www.math.com/tables/geometry/circles.htm

circumference: the distance around the circle
Circumference of Circle = PI x diameter = 2 PI x radius

So I insisted on 81 (A)
Director
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[#permalink]  05 May 2005, 22:38
Area of sq = 12*12
Area of Circle = 4/pi ^ 2

number of non-overlapping circles = 36* pi ^2

IMO AC's or the question is not correct.

B will be my guess
CIO
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[#permalink]  05 May 2005, 23:13
i'm agreeing with lovely. I think it's 81, A.

The diameter of each circle is 3pi, and if the side of the square is 12, then no more than nine circles can line up on a side. That's nine in each direction, which means 81 all together.
CIO
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[#permalink]  06 May 2005, 05:39
lovely_baby wrote:
To Ian7777
isn't the diametr=4/Pi

absolutely. thats what's on my paper. I just copied it wrong.

sorry 'bout that...
Director
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[#permalink]  06 May 2005, 05:59
ian7777 wrote:
i'm agreeing with lovely. I think it's 81, A.

The diameter of each circle is 3pi, and if the side of the square is 12, then no more than nine circles can line up on a side. That's nine in each direction, which means 81 all together.

\
pls explain how you got 3pi for the diamater of each circle. I got 4/pi
Current Student
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[#permalink]  06 May 2005, 14:11
A it is....

I narrowed it to B

lets say circumfrance is pi*D=4 lets estimate that d then is 2!

then in that case we will have 36 nonover lapping circles.

if we assume that Diameter was 1, then we would have 144 non-overlapping circles...
so the real answer is greater than 36 and less than 144....only A seems to be in that ball park!

A it is..
[#permalink] 06 May 2005, 14:11
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# 4965 PS > Geometry > Mixed Shapes How many

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