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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

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by oquiella » Tue Dec 22, 2015 3:11 pm

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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. 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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Source: Beat The GMAT — Problem Solving | Tue Dec 22, 2015 3:11 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 am; Location: https://martymurraycoaching.com/; Thanked: 955 times; Followed by:140 members; GMAT Score:800

by MartyMurray » Tue Dec 22, 2015 11:16 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. âˆš3:1
B. 1:1
C. 1/2:1
D. âˆš2:1
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.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Apr 27, 2018 9:37 am

oquiella 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. Square root 3:1
B. 1:1
C. 1/2:1
D. Square root 2:1
E. 2:1

If a right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere, then the height of the cone is exactly the radius of the hemisphere. So the ratio is 1:1.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]