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Q.

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter 4 units of the hemisphere are equal to the edge of the cube. What is the surface area of the remaining solid?


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a

2(24+π)   unit s 2  

b

4(24+π)   unit s 2  

c

4(12+π)   unit s 2  

d

2(14+π)   unit s 2   

answer is B.

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Detailed Solution

Given that the diameter 4 units of the hemisphere are equal to the edge of the cube.
We have the following formula,
Surface area of the cube =6 a 2  
Area of circle = π r 2  
Area of = 2π r 2  
Radius of the hemisphere will be 2cm.
The Surface area of remaining solid = surface area of cuboid box whose each of length 4-area of the top of the hemisphere part + even surface area of the hemisphere part
=6 (4) 2 −π 2 2 +2π 2 2 =6×16−π×4+2π×4 =96+4π =4(24+π)  units  2  
Thus, the surface area of the remaining solid is 4(24+π)   unit s 2  .
Therefore the correct option is 2.
 
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