Question

Please help me asap

Answer 1

`\textit{Volume of a Cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=13 \end{cases}\implies V=\pi r^2 13\implies 13\pi r^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{Volume of a Cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=16 \end{cases}\implies V=\cfrac{\pi r^2 (16)}{3}\implies V=\cfrac{16\pi r^2}{3} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{combined volumes}}{13\pi r^2~~ + ~~\cfrac{16\pi r^2}{3}}~~ = ~~6150\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 13\pi r^2~~ + ~~\cfrac{16\pi r^2}{3} \right)=3(6150)} \\\\\\ 39\pi r^2+16\pi r^2=18450\implies \stackrel{\textit{common factoring}}{r^2(39\pi +16\pi )}=18450\implies r^2(55\pi )=18450 \\\\\\ r^2=\cfrac{18450}{55\pi }\implies r^2=\cfrac{3690}{11\pi }\implies r=\sqrt{\cfrac{3690}{11\pi }}\implies \boxed{r\approx 10.33~m}`