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An artist is painting a white circular region on the top surface of a

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An artist is painting a white circular region on the top surface of a [#permalink]

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New post 14 Jun 2016, 12:28
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An artist is painting a white circular region on the top surface of a square blue tile that measures 8 inches on a side. If the circle is inscribed in the square, what fraction of the top surface of the tile will be blue?

A. \(\frac{1}{4}\)

B. \(\frac{1}{2}\)

C. \(\frac{\pi}{4}\)

D. \(\frac{(4 – \pi)}{\pi}\)

E. \(\frac{(4 – \pi)}{4}\)
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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New post 14 Jun 2016, 22:12
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It breaks down like this:
A circle inscribed in a square, means the circle touches all 4 inside edges of the square.
So if the square length is 8", so is the Diameter of the circle, which means the Radius is 4.
Area of a circle is πr^2 or in this case: π16"

So lets compare blue area to total area to get the final answer:
1) Area of Square - Area of the Circle = The Remaining Blue Area
64" - π16" = 64-π16 *Calculating this out at this point would be a mistake...

2) The Remaining Blue Area / Area of the Square = Answer
(64-π16) / 64 =(4-π1)/4 or (4-π)/4

Answer: E
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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New post 13 Nov 2016, 06:52
Hi mromrell,

I can't wrap my head around the last step you are doing.

We have the area of the square = 8*8 = 64
We also have the area of the circle = 4^2*π => 16π

Then the blue area must be = 64-16π

How do we go from this step to (4-π)/4 ?

Hope you can clarify, thanks!
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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saiesta wrote:
An artist is painting a white circular region on the top surface of a square blue tile that measures 8 inches on a side. If the circle is inscribed in the square, what fraction of the top surface of the tile will be blue?

A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(\frac{\pi}{4}\)
D. \(\frac{(4 – \pi)}{\pi}\)
E. \(\frac{(4 – \pi)}{4}\)


Attachment:
Untitled.png
Untitled.png [ 4.38 KiB | Viewed 2259 times ]


Area of Square is \(8^2\) = 64

Area of circle is \(π*4^2\) = \(16π\)

Area of Blue region is \(64 - 16π\)

So, Fraction of tile that will be Blue is = \(\frac{64 - 16π}{64}\)

Or, Fraction of tile that will be Blue is = \(\frac{16 (4 - π)}{16*4}\) = \(\frac{4 - π}{4}\)

Hence, Correct answer will be (E) \(\frac{4 - π}{4}\)
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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New post 17 Nov 2016, 09:45
Abhishek009 wrote:
saiesta wrote:
An artist is painting a white circular region on the top surface of a square blue tile that measures 8 inches on a side. If the circle is inscribed in the square, what fraction of the top surface of the tile will be blue?

A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(\frac{\pi}{4}\)
D. \(\frac{(4 – \pi)}{\pi}\)
E. \(\frac{(4 – \pi)}{4}\)


Attachment:
Untitled.png


Area of Square is \(8^2\) = 64

Area of circle is \(π*4^2\) = \(16π\)

Area of Blue region is \(64 - 16π\)

So, Fraction of tile that will be Blue is = \(\frac{64 - 16π}{64}\)

Or, Fraction of tile that will be Blue is = \(\frac{16 (4 - π)}{16*4}\) = \(\frac{4 - π}{4}\)

Hence, Correct answer will be (E) \(\frac{4 - π}{4}\)


Hi Abhishek009

Thank you very much for the explanation. I misread the question. I thought that we were being asked for the blue area, but I see now that we HAVE to divide by 64 as we are being asked for the fraction of the blue area to the square.
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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New post 17 Nov 2016, 10:26
Circle inscribed in a square=> diamter of circle = side of quare

Fraction of Blue area = (area of Square-Area of Circle)/Area of Square
= (8^2-pi*4^2)/8^2 = (4-pi)/4
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Re: An artist is painting a white circular region on the top surface of a [#permalink]

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New post 29 Jan 2018, 06:56
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Re: An artist is painting a white circular region on the top surface of a   [#permalink] 29 Jan 2018, 06:56
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