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A right circular cone is inscribed in a hemisphere so that

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A right circular cone is inscribed in a hemisphere so that [#permalink] New post 03 Apr 2012, 16:49
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A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

A. \sqrt{3} : 1

B. 1 : 1

C. \frac{1}{2} : 1

D. \sqrt{2} : 1

E. 2 : 1

I've never heard of a "hemisphere". I know that the cone forms a 30-60-90 right triangle and therefore the height of the cone is /3 but because I don't know what to do with the hemisphere, I'm stuck.

Thanks,
Rich
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Apr 2012, 00:23, edited 1 time in total.
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Re: Quick Question: "Hemisphere" [#permalink] New post 03 Apr 2012, 17:41
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A hemisphere is half of a sphere.

A right cone does not necessarily form a 30-60-90 triangle. In this case, the cone's is formed from an a isosceles right triangle rotated about the center - so the radius of the cone's base (also the hemisphere's base) = the height of the cone.

1:1 ratio - B

I noticed some "gimme" geometry problem on my exams - learn this stuff well & you can shave minutes off the time spent on geometry questions.
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Re: Quick Question: "Hemisphere" [#permalink] New post 03 Apr 2012, 20:18
nsspaz151 wrote:
A hemisphere is half of a sphere.

A right cone does not necessarily form a 30-60-90 triangle. In this case, the cone's is formed from an a isosceles right triangle rotated about the center - so the radius of the cone's base (also the hemisphere's base) = the height of the cone.

1:1 ratio - B

I noticed some "gimme" geometry problem on my exams - learn this stuff well & you can shave minutes off the time spent on geometry questions.


I take back what I said regarding the 30-60-90 triangle, that was a silly assumption on my part.

Thanks for the explanation regarding the hemisphere, it's so simple!
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Re: A right circular cone is inscribed in a hemisphere so that [#permalink] New post 04 Apr 2012, 00:48
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NvrEvrGvUp wrote:
A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?

A. \sqrt{3} : 1

B. 1 : 1

C. \frac{1}{2} : 1

D. \sqrt{2} : 1

E. 2 : 1

I've never heard of a "hemisphere". I know that the cone forms a 30-60-90 right triangle and therefore the height of the cone is /3 but because I don't know what to do with the hemisphere, I'm stuck.

Thanks,
Rich


As mentioned above hemisphere is just a half of a sphere. Now, since the cone is a right circular cone, the vertex of the cone must touch the surface of the hemisphere directly above the center of the base, which makes the height of the cone also the radius of the hemisphere.

Answer: B.
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Re: A right circular cone is inscribed in a hemisphere so that [#permalink] New post 23 Nov 2012, 02:10
Not sure if anyone else was scratching their heads wondering why the height couldn't be less than the radius, but just in case... it has to do with the word "inscribed": to draw within a figure so as to touch in as many places as possible <a regular polygon inscribed in a circle>

lol.
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Re: Quick Question: "Hemisphere" [#permalink] New post 04 Jan 2013, 09:23
nsspaz151 wrote:
A hemisphere is half of a sphere.

A right cone does not necessarily form a 30-60-90 triangle. In this case, the cone's is formed from an a isosceles right triangle rotated about the center - so the radius of the cone's base (also the hemisphere's base) = the height of the cone.

1:1 ratio - B

I noticed some "gimme" geometry problem on my exams - learn this stuff well & you can shave minutes off the time spent on geometry questions.


"gimme" geometry problems? might be because I'm new on the forum, but can you tell me what are you referring to?
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Re: Quick Question: "Hemisphere" [#permalink] New post 04 Jan 2013, 10:12
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sianissimo wrote:
nsspaz151 wrote:
A hemisphere is half of a sphere.

A right cone does not necessarily form a 30-60-90 triangle. In this case, the cone's is formed from an a isosceles right triangle rotated about the center - so the radius of the cone's base (also the hemisphere's base) = the height of the cone.

1:1 ratio - B

I noticed some "gimme" geometry problem on my exams - learn this stuff well & you can shave minutes off the time spent on geometry questions.


"gimme" geometry problems? might be because I'm new on the forum, but can you tell me what are you referring to?


"Gimme" is slang for quick/easy. If you know geometry well, you can avoid doing any calculation on some problems.
Re: Quick Question: "Hemisphere"   [#permalink] 04 Jan 2013, 10:12
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