Question

How to find the area of this half a cone surface area solids with curved surfaces? Please give explanation and steps also formula!

Answer 1

Check the picture below.

we can think of this frustum as two cones, so let's simply get the whole surface area of the larger cone, and then subtract the lateral area of the smaller cone, so what's leftover is what we didn't subtract, the area at the bottom of the larger cone, and the base of the smaller cone.

`\textit{Surface area of the \underline{larger} Cone}\\\\ SA=\pi rs + \pi r^2~~ \begin{cases} r=radius\\ s=\textit{slant height}\\[-0.5em] \hrulefill\\ r=4.5\\ s=6 \end{cases} \implies SA=\pi (4.5)(6)+\pi (4.5)^2 \\\\\\ SA=27\pi +20.25\pi \implies SA=47.25\pi ~m^2 \\\\[-0.35em] ~\dotfill`

`\textit{Lateral area of the \underline{smaller} Cone}\\\\ LA=\pi rs ~~ \begin{cases} r=radius\\ s=\textit{slant height}\\[-0.5em] \hrulefill\\ r=1.5\\ s=2 \end{cases} \implies LA=\pi (1.5)(2)\implies LA=3\pi \\\\[-0.35em] ~\dotfill\\\\ 47.25\pi~~ - ~~3\pi\implies 44.25\pi ~~ \approx ~~ \text{\LARGE 139.06}~m^2`