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Naveen Biddu

· started a discussion

· 1 Months ago

whats answer (Question:857791.0)

plzzz check options and detail of solution

Question:

The radius of a cone is  2    time the height of the cone. A cube of maximum possible volume is cut from the same cone. What is the ratio of the volume of the cone to the volume of the cube 

Options:
A)

3.18 π   

B)

2.25 π   

C)

2.35 π   

D)

Can’t be determined

Solution:

  

Let the each side of cube be a, 

then CD =  2a   

∴CQ=a2    

Let the radius of cone be r and height be h, then 

r =  h2   

∴    In  ΔAPO    and  ΔCQO    (similar triangle)  

⇒APPO=CQOQ=rh=a2h–a    

a2h–a=2    

a = 2(h – a)  

h=32a   ,  r=32a2   

∴    Volume of cone =    

=  94a3π   

and volume of cube = a3

∴    Required Ratio =  94πa3   

  

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