Question

A pentagonal pyramid has a volume of 1536 in3. What is the volume of the pentagonal pyramid if the measures are multiplied by 1/4 ?

Answer 1

`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=base\\ h=height\\ ----------\\ B=(1)/(4)B\\\\ h=(1)/(4)h \end{cases}\implies 1536=\cfrac{1}{3}Bh \\\\\\ V=\cfrac{1}{3}\cdot \cfrac{B}{4}\cdot \cfrac{h}{4}\implies V=\cfrac{1}{3}Bh\cdot \cfrac{1}{4\cdot 4}\implies V=\cfrac{1}{3}Bh\cdot \cfrac{1}{16} \\\\\\ V=\cfrac{(1)/(3)Bh}{16}\impliedby (1)/(16)th\textit{ of the original}`