Question

Question 5
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Answer 1

The diameter of hemisphere = edge of the cube = l.
The radius of the hemisphere = l / 2.
Total surface area of solid = Surface area of cubical part + CSA of hemispherical part - Area of base of hemispherical part
$=(6\times edg{e}^2)+\left(2\pi r^2\right)-\left(\pi r^2\right)=6\times edg{e}^2+\pi r^2$
Total surface area of solid $=6\times l^2+\pi \times (l/2{)}^2$
$=6\times l^2+\frac{\pi \times l^2}{4}$
$=\frac{1}{4}\times (24+\pi )\times l^{2}uni{t}^2$