Question

Two right circular cylinders have equal volume. The first cylinder has a radius of 6 inches and a height of 12 inches. What is the number of inches in the height of the second cylinder if its radius is 8 inches

Answer 1

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r = 6\\ h = 12 \end{cases}\implies \stackrel{\textit{~\hfill volume of the 1st cylinder}}{V=\pi (6)^2(12)\implies V=\underline{432\pi} } \\\\[-0.35em] ~\dotfill$

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r = 8\\ \stackrel{equal~volumes}{V=\underline{432\pi}~\hfill } \end{cases}\implies 432\pi =\pi (8)^2 h \\\\\\ 432\pi =64\pi h\implies \cfrac{432\pi }{64\pi }=h\implies \cfrac{27}{4}\implies 6\frac{3}{4}=h$