Question

The dimensions of a triangular prism are tripled. How will the changes in the prism’s dimensions affect the volume of the prism?

Answer 1

a triangular prism, like the one in the example in the picture below, has a volume of the area of the triangle times the length, namely (1/2)bh * L.

now, if b, h and L were tripled, how would the new volume change in relation to the original volume?

$\bf \textit{volume of a triangular prism}\\\\ V=\cfrac{1}{2}bh\cdot L~~ \begin{cases} L=length\\ b=base\\ h=height\\[-0.5em] \hrulefill\\ L=3L\\ b=3b\\ h=3h \end{cases}\implies V=\cfrac{1}{2}(3b)(3h)(3L) \\\\\\ V=(3)(3)(3)\cfrac{1}{2}bh\cdot L\implies \stackrel{\textit{27 times that of the orginal}}{V=27\left( \cfrac{1}{2}bh\cdot L \right)}$