Answer to Question #148831 in Geometry for anlp

Question

A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the diagonal of the rectangular solid?

Answer 1

To find diagonal of the rectangular solid, we need to use two times Pythagorean theorem:

Firstly, let`s to find diagonal of base from Pythagorean:

$a^2+b^2=c^2$ we have givan values of of base of rectangular solid and it`s height:

diagonal of base = $\sqrt{\smash[b]{a^2+b^2}}=\sqrt{\smash[b]{4^2+8^2}}=8.94$.

Secondly, we find diagonal of solid by also Pythagorean:

diagonal of rectangular = $\sqrt{\smash[b]{a^2+b^2}}=\sqrt{\smash[b]{8.94^2+12^2}}=14.96$.

Diagonal of rectangular solid is 14.96.