Answer to Question #150233 in Geometry for solid mensuration

Question

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

a) 7.49 cm
b) 8.94 cm
c) 14.42 cm
d) 14.97 cm

Answer 1

Let $a=$ the length of a rectangular solid, $b=$ its width, a $c=$ its height.

The the diagonal $d$ of a rectangular solid will be

$$d=\sqrt{a^2 +b^2+c^2}$$ $$d=\sqrt{4^2+8^2+12^2}=4\sqrt{14}(cm)\approx14.97(cm)$$

d) 14.97 cm