Question #148831
A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the diagonal of the rectangular solid?
1
Expert's answer
2020-12-11T09:48:44-0500

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:

a2+b2=c2a^2+b^2=c^2 we have givan values of of base of rectangular solid and it`s height:

diagonal of base = a2+b2=42+82=8.94\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 = a2+b2=8.942+122=14.96\sqrt{\smash[b]{a^2+b^2}}=\sqrt{\smash[b]{8.94^2+12^2}}=14.96.

Diagonal of rectangular solid is 14.96.


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