Question

A pen talking pyramid has a volume of 1536in what is the volume of the pentagonal pyramid if measures are multiplied by 1/4

Answer 1

$\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of its base}\\ h=height\\ ----------\\ B=\frac{1}{4}B\\\\ h=\frac{1}{4}h \end{cases}\implies V=\cfrac{1}{3}\cdot \cfrac{B}{4}\cdot \cfrac{h}{4} \\\\\\ V=\cfrac{1}{3}\cdot \cfrac{1}{4\cdot 4}Bh\implies V=\cfrac{1}{16}\left( \cfrac{1}{3}Bh \right)$

so, you'd end up with a pyramid with a volume "one sixteenth" of the original then

now, the original had a volume of 1536, the quarterized version will then just be one sixteenth of that, or 1536 * 1/36