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Q.

Find the volume of the greatest sphere that can be cut from a cylindrical log of wood of base radius 1 cm   and height 5 cm.  


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a

4 5 πc m 3  

b

4 3 πc m 3  

c

4 3 c m 3  

d

4 21 c m 3   

answer is B.

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Detailed Solution

Given that, base of log of wood is 1cm and height 5cm.
The volume of the sphere = 4 3 ×π× r 3  
Draw the required diagram,
Question ImageThe radius of the sphere = Radius of cylindrical log of wood
The volume of the sphere is,
⇒ 4 3 ×π× 1 3 ⇒ 4 3 πc m 3  
Thus, the volume of the greatest sphere is 4 3 πc m 3  .
Therefore, option (2) is correct.
 
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