Question

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Answer 1

Diameter of hemisphere = Edge of cube =$l$
Radius of hemisphere =$\frac{ l}{2}$

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part
$= 6 (\text{edge})^2+2\pi r^2-\pi r^2$
$= 6l^2 \+ \pi r^2$
$= 6l^2+\pi(\frac{l}{2})^2$
$= 6l^2+\frac{\pi l^2}{4}$
$=\frac{ l^2}{4}(24+\pi )$ sq. units