How big is this circumsphere?

Geometry Level pending

The problem's question: How big is this circumsphere?

The 5 4-dimensional points on the surface of the hyper-sphere are:

{9,6,6,3},{7,8,6,3},{7,6,8,3},{7,6,6,5} and {8,7,7,4}

The volume is in $\mathbb{R}^4$ volume units as this is actually a 4-dimensional hyper-sphere. The value of $\pi$ has not been divided out of the answer. Therefore, you need to include $\pi$ in the appropriate manner. You do not need to determine the center of the hyper-sphere to answer this problem, only the radius.

The answer is 78.9568352087149.

1 solution

A Former Brilliant Member
Mar 10, 2019

$\text{Sphere}[\{7,6,6,3\},2]$ . The radius is 2. The volume is $\frac{\pi ^2 2^4}{2} \Longrightarrow 78.9568352087149$ .

The W. H. Beyer method for solving a circumsphere works on this problem.

How big is this circumsphere?

The answer is 78.9568352087149.

1 solution

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