Rectangular parallelepiped

Statement

Given a rectangular parallelepiped with dimensions $3\times 4\times 12$, calculate its volume, total surface area and diagonal.

Solution

With $a=3$, $b=4$, $c=12$: $V = abc = 3\cdot 4\cdot 12 = \boxed{144}.$ $S_{\text{tot}} = 2(ab+bc+ca) = 2(12+48+36) = \boxed{192}.$ $d = \sqrt{a^2+b^2+c^2} = \sqrt{9+16+144} = \sqrt{169} = \boxed{13}.$

Links

Topics: Synthetic geometry in space
Concepts: Parallelepiped · Surface area · Volume
Skills: Calculating · Using formulae
Exercise types: Geometric problem