Question

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

Answer 1

Given:
Diameter of hemisphere = Edge of the cube $=l$
Radius of hemisphere $r=\frac{l}{2}$
Total surface area of solid = Surface area of cubical part + Closed Surface of hemisphere part - Area of base of hemispherical part

$=6(Edge{)}^2+2\pi r^2-\pi r^2=6(Edge{)}^2+\pi r^2$

Total surface are of solid = $6l^2+\pi \times {\left(\frac{l}{2}\right)}^2$
= $6l^2+\frac{\pi l^2}{4}$

$=\frac{1}{4}[24+\pi ]l^2$ sq. units