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Lera25 [3.4K]
2 years ago
12

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

Mathematics
1 answer:
Natasha2012 [34]2 years ago
7 0
\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
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