Question

Having trouble understanding this

Answer 1

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=2 \end{cases}\implies 192\pi =\cfrac{\pi 2^2 h}{3} \\\\\\ 192\pi =\cfrac{4\pi h}{3}\implies \cfrac{ 3}{4\pi }\cdot 192\pi=h\implies 144=h \\\\[-0.35em] ~\dotfill`

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=3 \end{cases}\implies 192\pi =\cfrac{\pi 3^2 h}{3} \\\\\\ 192\pi =3\pi h\implies \cfrac{192\pi }{3\pi }=h\implies 64=h \\\\[-0.35em] ~\dotfill`

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=4 \end{cases}\implies 192\pi =\cfrac{\pi 4^2 h}{3} \\\\\\ 192\pi =\cfrac{16\pi h}{3}\implies \cfrac{ 3}{16\pi }\cdot 192\pi=h\implies 36=h`