Question

5. A hemispherical depression is cut out from one face of a cubical wooden block such
that the diameter 1 of the hemisphere is equal to the edge of the cube. Determine the
surface area of the remaining solid.​

Answer 1

Answer

Consider the diagram shown below.

It is given that a hemisphere of radius 2l is cut out from the top face of the cuboidal wooden block.

Therefore, surface area of the remaining solid

= surface area of the cuboidal box whose each edge is of length l − Area of the top of the hemispherical part + curved surface area of the hemispherical  part

=6l2−πr2+2πr2

=6l2−π(2l)2+2π(2l)2

=6l2−4πl2+2πl2

=4l2(24+π) sq.units