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

After cutting out a hemispherical depression, the view of the surface looks like this.



The diameter of the hemisphere isunits.

Thus, the side of the cube is also  units.

The surface area of each of the other 5 faces of the cube is.

For the face from which a hemisphere has been cut, subtract the area of a circle of diameterunits fromand then add the area of a hemisphere of diameterunits to it.

Area a circle of diameterunits is.

Surface Area of a hemisphere of diameterunits is

 

That is the surface area of the face from which a hemisphere has been cut is:

 

Thus, the total surface area of the remaining solid is: 



Therefore, the total surface area of the remaining solid is

 

Answer 2

Answer:

Step-by-step explanation: