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# A right circular cone is such that it perfectly fits inside a hollow

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Math Expert
Joined: 02 Sep 2009
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A right circular cone is such that it perfectly fits inside a hollow  [#permalink]

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23 Jul 2017, 23:23
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:28) correct 45% (01:16) wrong based on 80 sessions

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A right circular cone is such that it perfectly fits inside a hollow sphere. What is the height of the cone?

(1) The radius of the sphere is 6.
(2) The radius of the cone is 4.

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A right circular cone is such that it perfectly fits inside a hollow  [#permalink]

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24 Jul 2017, 07:36
1
Bunuel wrote:
A right circular cone is such that it perfectly fits inside a hollow sphere. What is the height of the cone?

(1) The radius of the sphere is 6.
(2) The radius of the cone is 4.

It should be C.

Statement 1: Insufficient

We do not know the anything about the height of the base of the cone from base of the sphere (distance DE in the picture attached). Nor do we know anything about the sphere.

Statement 2: Insufficient

We have no idea of diameter of sphere.

Combined. We have Hypotenuse and base of triangles OBD and OCD in the picture. We can calculate distance to centre O (measurement X). X added to radius should give height of the cone.

Note: this diagram is purely for educational purposes and any symbolism is completely unintentional.
Attachments

cone.jpg [ 51.68 KiB | Viewed 799 times ]

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Re: A right circular cone is such that it perfectly fits inside a hollow  [#permalink]

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24 Jul 2017, 08:41
Bunuel wrote:
A right circular cone is such that it perfectly fits inside a hollow sphere. What is the height of the cone?

(1) The radius of the sphere is 6.
(2) The radius of the cone is 4.

Best way forward to solve this question is by drawing figures.

Posted from my mobile device
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File comment: www.GMATinsight.com

IMG_20170724_210907.jpg [ 2.8 MiB | Viewed 740 times ]

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Re: A right circular cone is such that it perfectly fits inside a hollow  [#permalink]

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01 Jan 2019, 08:22
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Re: A right circular cone is such that it perfectly fits inside a hollow   [#permalink] 01 Jan 2019, 08:22
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