Question

A cylinder with a diameter of 10 mm has a surface area of 439.83 mm². Find the volume of the cylinder.

Answer 1

well, we know the diameter is 10, so the radius is half that or 5.

`\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ SA=439.83 \end{cases}\implies 439.83=2\pi (5)(h+5) \\\\\\ 439.83=10\pi (h+5)\implies \cfrac{439.83}{10\pi }=h+5\implies \cfrac{439.83}{10\pi }-5=h \\\\[-0.35em] ~\dotfill`

`\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5 \end{cases}\implies V=\pi (5)^2h\implies V=25\pi h \\\\\\ \stackrel{\textit{substituting from above}}{V=25\pi\left( \cfrac{439.83}{10\pi }-5 \right)}\implies V=1099.575-125\pi \implies \boxed{V\approx 706.88~mm^3}`