Question

A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?

Answer 1

`\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height\\ ----------\\ h=12\\ V=236 \end{cases}\implies 236=\cfrac{1}{3}B(12) \\\\\\ 3\cdot 236=12B\implies \cfrac{708}{12}=B\implies 59=B`

now, is a square pyramid, like the picture below, so the base is just a square, so B = length * width, thus


`\bf B=length\cdot width\quad \begin{cases} length=x\\ width=x\\ B=59 \end{cases}\implies B=x\cdot x\implies B=x^2 \\\\\\ 59=x^2\implies √(59)=x`