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

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

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 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; 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. √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.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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]

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