# Thread: Diameter of inscribed sphere

1. ## Diameter of inscribed sphere

A new one just for fun and the curious.

SphereDiameter.jpg

2. I get 3 * (square root of 3/2), but apparently I'm wrong.

Seems to me the trick is to get the length of one side, which will be the diameter of the sphere. They give you the length from corner to corner, and then you use the formula for a right triangle to get the sides.

3. mrjimphelps: you are on the right track.

4. Originally Posted by mrjimphelps
They give you the length from corner to corner, and then you use the formula for a right triangle to get the sides.
Yes, but beware it's not an equilateral right triangle.

The diameter of the sphere is the same as the length of one side of the cube. That's one side of your right triangle. The other side of the right triangle is a diagonal across one face of the cube, and the hypotenuse is the diameter of the cube, which is given.

5. DG1261: Correct...Californians hit it first crack. :-)

6. Solved using a different method

7. That's actually the way most HS students are taught to solve this problem, Maud.
If the object were a rectangular solid, the same thinking applies. Then, in reverse, the long diagonal is the sqrt of the sum of the squares of the side lengths.

8. That's actually the way most HS students are taught to solve this problem
In our day.... They're learning this stuff in grade school now!

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