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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]

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Updated on: 10 Jun 2012, 22:12
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Difficulty:

15% (low)

Question Stats:

81% (01:25) correct 19% (01:25) wrong based on 31 sessions

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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?

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Originally posted by alchemist009 on 10 Jun 2012, 17:43.
Last edited by Bunuel on 10 Jun 2012, 22:12, edited 2 times in total.
Edited the question.
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Re: hemisphere inscribed in a circle  [#permalink]

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10 Jun 2012, 19:43
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Re: hemisphere inscribed in a circle  [#permalink]

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10 Jun 2012, 19:56
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]

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11 Jun 2012, 21:01
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]

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14 Oct 2019, 14:02
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Re: The base of a hemisphere is inscribed in one face of a cube   [#permalink] 14 Oct 2019, 14:02
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