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OG 13 20

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oquiella Master | Next Rank: 500 Posts Default Avatar
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OG 13 20

Post Tue Dec 22, 2015 3:11 pm
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. Square root 3:1
B. 1:1
C. 1/2:1
D. Square root 2:1
E. 2:1


Answer: B


Please explain reasoning

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Post Tue Dec 22, 2015 11:16 pm
Quote:
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. √3:1
B. 1:1
C. 1/2:1
D. √2:1
E. 2:1
The height of the cone goes from the center of the base of the hemisphere to the surface of the hemisphere. That's the radius of the hemisphere.



So the height of the cone is the same as the radius of the hemisphere, and therefore the ratio of the height of the cone to the radius of the hemisphere is 1:1.

The correct answer is B.

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