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The base of a hemisphere is inscribed in one face of a cube

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The base of a hemisphere is inscribed in one face of a cube [#permalink] New post 10 Jun 2012, 16:43
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The base of a hemisphere is inscribed in one face of a cube and the entire hemisphere in contained within the volume of the cube. What is the ratio of the radius of the hemisphere to the length of a side of the cube?

A. \(\sqrt{2}:P\)
B. \(1:2\)
C. \(2:P\)
D. \(1:\sqrt{2}\)
E. \(2:1\)

here i found that logically D=S or 2r=S SO r/s= 1/2 ....is my reason correct?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 10 Jun 2012, 21:12, edited 2 times in total.
Edited the question.
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Re: hemisphere inscribed in a circle [#permalink] New post 10 Jun 2012, 18:43
Your reasoning is correct.
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Re: hemisphere inscribed in a circle [#permalink] New post 10 Jun 2012, 18:56
Also, the whole cube/hemisphere is a bit of a misnomer. The situation really is just a circle inscribed in a square. Once you draw that, it's easy to get B
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Re: The base of a hemisphere is inscribed in one face of a cube [#permalink] New post 11 Jun 2012, 20:01
Expert's post
alchemist009 wrote:
The base of a hemisphere is inscribed in one face of a cube and the entire hemisphere in contained within the volume of the cube. What is the ratio of the radius of the hemisphere to the length of a side of the cube?

A. \(\sqrt{2}:P\)
B. \(1:2\)
C. \(2:P\)
D. \(1:\sqrt{2}\)
E. \(2:1\)

here i found that logically D=S or 2r=S SO r/s= 1/2 ....is my reason correct?


Check out Brian's video on 'circle in a square' and 'square in a circle'.
http://www.veritasprep.com/blog/2011/06 ... in-shapes/
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Re: The base of a hemisphere is inscribed in one face of a cube [#permalink] New post 25 Sep 2014, 12:20
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Re: The base of a hemisphere is inscribed in one face of a cube   [#permalink] 25 Sep 2014, 12:20
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