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A rectangular solid, 3 x 4 x 12, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is

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by BTGmoderatorLU » Sun Feb 07, 2021 11:36 am
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A rectangular solid, 3 x 4 x 12, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is the diameter of the sphere?

A. 13
B. 15
C. 18
D. 19
E. 20

The OA is A
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Re: A rectangular solid, 3 x 4 x 12, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What

by Scott@TargetTestPrep » Tue Feb 23, 2021 5:38 am
BTGmoderatorLU wrote: ↑
Sun Feb 07, 2021 11:36 am
 Source: Magoosh

A rectangular solid, 3 x 4 x 12, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is the diameter of the sphere?

A. 13
B. 15
C. 18
D. 19
E. 20

The OA is A
Solution:

If a rectangular solid is inscribed in a sphere, then its space diagonal is the diameter of the sphere. Since the space diameter of a rectangular solid with dimensions 3 by 4 by 12 is √(3^2 + 4^2 + 12^2) = √169 = 13, the diameter of the circumscribed sphere is also 13.

Answer: A

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