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.


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Answer:

 

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.
    l l l _ 2 l _ 2 l _ 2 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.

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