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A circular mat with diameter 20 inches is placed on a square

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A circular mat with diameter 20 inches is placed on a square [#permalink] New post 26 Aug 2010, 06:34
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A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6
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A circular mat with diameter 20 inches is placed on a square [#permalink] New post 26 Aug 2010, 07:37
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udaymathapati wrote:
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose
sides is 24 inches long. Which of the following is closest to the fraction of the tabletop
covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6


\(area_{circle}=\pi{r^2}=\pi{10^2}\approx{314}\) (\(d=20\) --> \(r=10\));

\(area_{square}=24^2=576\);

\(\frac{area_{circle}}{area_{square}}=\frac{314}{576}=\frac{157}{288}\).

Now this fraction is obviously between 1/2 and 3/4 --> \(\frac{1}{2}=\frac{144}{288}\) and \(\frac{3}{4}=\frac{216}{288}\) --> 157 is closer to 144 than to 216.

Answer: C.
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Re: Closest Fraction Calculation Problem [#permalink] New post 27 Aug 2010, 04:29
Nice explanation Bunuel... Thanks
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Re: GWD #1 Math 7 [#permalink] New post 05 Apr 2012, 11:49
SO we are looking for the area of the cloth over the area of the table

Area of the Cloth = (pi)(r)^2 which is about (3)(10)(10)

Area of the Table = (24)(24)

So the quick way to estimate is looking at the fraction like this: (3/24)(100/24)

I hope this is easy to follow, so with some simplification i get (1/8)(4) = (1/2) Answer is C
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 04 May 2013, 03:07
Hi Bunel
Please let me clarify how did you establish 1/2=144/288 and 1/3= 216/288???

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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 04 May 2013, 03:31
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 29 Jul 2013, 01:25
udaymathapati wrote:
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?

A. 5/12
B. 2/5
C. 1/2
D. 3/4
E. 5/6

Simplified the numbers as below:
Req fraction is (3.14 * 10 * 10)/(24 * 24)
Cancel 10 and 24 by 2: (3.14 * 5 * 5)/(12 * 12)
Cancel 5*5=25 in numerator with 12 in denominator: (3.14 * 2.something)/(1 * 12) = 6.something / 12 =~1/2. (Here it is important to note that 2.something and 6.something are in the lower end, i.e., much lesser than 2.5 and 6.5.)
Bunuel has given a standard way to deal with fraction comparison in the previous posts. In some cases, the above sort of simplifications might help in getting a fraction with realtively smaller numerator and denominators.
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 25 Feb 2015, 21:35
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Re: A circular mat with diameter 20 inches is placed on a square [#permalink] New post 04 Nov 2015, 13:41
if D = 20, then r = 10, and area of the circle is 100 pi (I converted pi to 22/7) and thus the area is 2200/7
area of the square is 24^2 = 576
now, to find the area that is covered by the circle, divide 2200/7 by 576. get 2200/4032, which is slightly more than 1/2.

other method, 2200/7 is slightly more than 300
300+/576 = aprox 1/2
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A circular mat with diameter 20 inches is placed on a square [#permalink] New post 21 Nov 2015, 19:42
I don't get why everyone is over-complicating the math here since the question stem clearly asks to ESTIMATE.

Making pi = 3

Area of circle = 2*5*2*5*3
Area of sqr = 12*3*2*2

3s cancel. 4s cancel. left with 25/48 close to 25/50 = 1/2
A circular mat with diameter 20 inches is placed on a square   [#permalink] 21 Nov 2015, 19:42
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