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20 Apr 2011, 09:47
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I often spend way too much time re-solving for these, each time I encounter them.
Circle Inscribed In A Square
The circle will have radius r, and consequentially the square will have side 2r.
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 4r^2, or (pi)/4
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 8r, or (pi)/4
Conveniently, the ratios are both the same!
The difference in area is (4-pi)*r^2
The difference in perimeter is (8-2pi)*r
Square Inscribed in a circle
This one is harder to solve for, since you have to do some calculations to solve for either the radius or the side of a square.
Assuming the circle has radius r, and the square will have side r*sqrt(2).
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 2r^2, or (pi)/2
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 4r*sqrt(2), or (pi)/(2*sqrt(2))
The difference in area is (pi-2)*r^2
The difference in perimeter is (2pi - 4*sqrt(2))*r
Circle Inscribed In A Square
The circle will have radius r, and consequentially the square will have side 2r.
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 4r^2, or (pi)/4
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 8r, or (pi)/4
Conveniently, the ratios are both the same!
The difference in area is (4-pi)*r^2
The difference in perimeter is (8-2pi)*r
Square Inscribed in a circle
This one is harder to solve for, since you have to do some calculations to solve for either the radius or the side of a square.
Assuming the circle has radius r, and the square will have side r*sqrt(2).
What this means, is:
Ratio of area of circle to area of square = (pi)r^2 to 2r^2, or (pi)/2
Ratio of perimeter of circle to perimeter of square = 2(pi)r to 4r*sqrt(2), or (pi)/(2*sqrt(2))
The difference in area is (pi-2)*r^2
The difference in perimeter is (2pi - 4*sqrt(2))*r
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
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20 Jun 2017, 10:23
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Automated notice from GMAT Club BumpBot:
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
