since it's diameter is 24, its radius must be 12.
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies SA=4\pi (12)^2\implies SA=576\pi[/tex]
now, that's for a sphere, for a hemisphere with the same radius it'd just be half that or 288π, now let's add the area of the circular base.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{hemisphere}{288\pi} ~~ + ~~\stackrel{circular~base}{\pi (12)^2}}\implies 288\pi ~~ + ~~144\pi \implies 432\pi[/tex]
The total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.
A hemisphere is "half the part of sphere".
According to the question,
The diameter of greater circle is 24 this implies radius of circle is 12.
Surface area of sphere = 4πr²
= 4×π × (12)²
= 576π.
Surface area of sphere is 576π
Surface area of Hemisphere is half of the surface area of sphere.
(576π)/2 = 288π
In order to include the base in the total area only if add surface area of hemisphere and area of circle.
surface area of hemisphere + rea of circle = 288π + π(r)²
= 288π + π(12)²
= 288π + 144π
= 432π
Hence, the total surface area of the hemisphere is 288π. The area that include both surface area of hemisphere and the base of the total area is 432π.
Learn more about hemisphere here
https://brainly.com/question/16724000
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