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Manager  Joined: 03 Jan 2015
Posts: 72
An artist is painting a white circular region on the top surface of a  [#permalink]

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11 00:00

Difficulty:   45% (medium)

Question Stats: 68% (01:51) correct 32% (01:51) wrong based on 238 sessions

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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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Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
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Re: An artist is painting a white circular region on the top surface of a  [#permalink]

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5
1
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 [ 4.38 KiB | Viewed 4712 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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Current Student B
Joined: 28 Mar 2016
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Re: An artist is painting a white circular region on the top surface of a  [#permalink]

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4
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

Intern  Joined: 26 Aug 2016
Posts: 3
Re: An artist is painting a white circular region on the top surface of a  [#permalink]

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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!
Intern  Joined: 26 Aug 2016
Posts: 3
Re: An artist is painting a white circular region on the top surface of a  [#permalink]

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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.
Manager  B
Joined: 03 Oct 2013
Posts: 77
Re: An artist is painting a white circular region on the top surface of a  [#permalink]

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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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_________________ Re: An artist is painting a white circular region on the top surface of a   [#permalink] 18 May 2019, 00:42
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