Surface of a Hemisphere

A solid hemisphere has two parts to its outside: the curved bowl, which is half a sphere's surface, and the flat circle where it was cut.

This hemisphere has radius 4. The bowl is half of $4\cdot \pi\cdot {4}^{2}$, so $2\cdot \pi\cdot 16 = 32\cdot \pi$. The flat circle is $\pi\cdot {4}^{2} = 16\cdot \pi$. Together they make 48π.

The rule is Surface area of a hemisphere: $SA = 3\cdot \pi\cdot {r}^{2}$, two circles' worth of bowl plus one circle of lid. Forgetting the flat circle is the usual slip.