Question

What is the total surface area of a hemisphere?

Answer 1

Write the total surface area of a hemisphere.

$\begin{array}{rcl}\mathrm{Total}\mathrm{surface}\mathrm{Area}& =& \mathrm{Curved}\mathrm{Surface}\mathrm{Area}+\mathrm{Base}\mathrm{Area}\\ & \Rightarrow & \mathrm{Total}\mathrm{surface}\mathrm{Area}=2{\mathrm{\pi r}}^2+{\mathrm{\pi r}}^2\\ & \Rightarrow & \mathrm{Total}\mathrm{surface}\mathrm{Area}=3{\mathrm{\pi r}}^2\end{array}$

Thus, a hemisphere's total surface area is equal to $3{\mathrm{\pi r}}^2$ square units.

Where $\mathrm{\pi }$ is a constant whose value is roughly equivalent to $3.14$ and the radius of the hemisphere is $r$.

Hence,total surface area of hemisphere is $3{\mathrm{\pi r}}^2$.