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

 l2 4
× (24 + π) sq.units

Step by Step Explanation:
1. Let us consider d be the diameter of hemisphere and l be the edge of the cube.
Here, it is given that the diameter of the hemisphere is equal to the edge of the cube.
So, the diameter of the hemisphere d = l . Where, the edge of the cube = l.
2. Now,
The total surface area of the cube after hemispherical depression = The total surface area of the cube - The base area of the hemisphere + The curved surface area of the hemisphere
= 6l2 - πr2 + 2πr2
= 6l2 + πr2
= 6l2 + π× (l/2)2
= 6l2 +
 π l2 4

=
 l2 4
(24 + π) sq.units
3. Thus, the total surface area of the cube after hemispherical depression is
 l2 4
(24 + π) sq.units.