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| Math Central | Quandaries & Queries |
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Question from Gelo, a student: What are the largest volume and total surface area of a cube that may be inscribed inside a sphere whose radius is 5 kilometers. |
The problem appears more complex than it is.
The cube has central symmetry - any two opposite vertices of the cube are connected by a diagonal which is also called the diameter of the cube.. The sphere also has central symmetry (opposite points).
So it is a matter of recognizing that the diameter of the sphere is the diameter of the largest cube.
The side dimension of this cube can be calculated using either a bit of trig, or a couple of steps with Pythagoras Theorem - and the rest follows.
Walter
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Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.