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.

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

The diameter of the hemisphere is units.

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 diameter units from and then add the area of a hemisphere of diameter units to it.

Area a circle of diameter units is .

Surface Area of a hemisphere of diameter units 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

 

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