check the picture below.
so, we have a cylinder with a height of 15.2 and a radius of 4.2, half of the diameter, however, the radius of the semi-sphere is also 4.2.
now, we have two semi-spheres, if we slap them together, well, that simply gives us a full sphere, that has a radius of 4.2, so to get the area of both semi-spheres, we can simply get the area of a full sphere.
[tex]\bf \textit{total surface area of a cylinder}\\\\
SA=2\pi r(h+r)~~
\begin{cases}
h=15.2\\
r=4.2
\end{cases}\implies SA=2\pi (4.2)(15.2+4.2)
\\\\\\
SA=8.4\pi(19.4)\implies \boxed{SA=162.96\pi} \\\\
-------------------------------\\\\
\textit{surface area of a sphere}\\\\
SA=4\pi r^2\qquad r=4.2\qquad SA=4\pi (4.2)^2\implies \boxed{SA=70.56\pi} [/tex]
add both SAs, and that's the surface area of the hmmm looks like a capsule, of the capsule.
