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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
An artist is painting a white circular region on the top surface of a
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29 Nov 2022, 08:23
29 Nov 2022, 08:23
Expert Reply
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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. \(\frac{(4 – \pi)}{4}\)
A. \(\frac{1}{4}\)
B. \(\frac{1}{2}\)
C. \(\frac{\pi}{4}\)
D. \(\frac{(4 – \pi)}{\pi}\)
E. \(\frac{(4 – \pi)}{4}\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: An artist is painting a white circular region on the top surface of a
[#permalink]
30 Nov 2022, 22:46
30 Nov 2022, 22:46
1
Expert Reply
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 let's compare the blue area to the 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
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 let's compare the blue area to the 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
gmatclubot
Re: An artist is painting a white circular region on the top surface of a [#permalink]
30 Nov 2022, 22:46
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