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A cube of wax is melted down and poured into a spherical mold. The wax perfectly fills half of the spherical mold (therefore taking the shape of a hemisphere).

Would the original cube of wax have fit inside the spherical mold (without changing the shape of the cube)?

 Feb 13, 2021
 #1
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The  volume  of the wax  cube  = S^3     where  S is the side  of  the  cube

 

The    length  of the  3D  diagonal vertex  of the  cube = sqrt (3) S  ≈  1.73S

 

The  diameter  of  the  sphere  must  be  greater  than  this  for  the  cube to fit inside the sphere

 

The volume of   the  hemisphere   =   (2/3)pi * r^3

 

Therefore

 

Volume of the  cube  =Volume of the hemisphere

 

S^3  =  (2/3)pi  *  r^3        solve for  r   

 

S^3 / [ (2/3)pi ]   =  r^3  take  the   cube root

 

S / [ (2/3)pi] ^(1/3)   =  r    ≈ .782 S

 

So  the diameter of the sphere = 2(.782) S  =  1.564S

 

So....the wax cube would not  fit

 

cool cool cool

 Feb 13, 2021

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