MathematicsHow many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, each bullet being 4 cm in diameter.

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, each bullet being 4 cm in diameter.


  1. A
    2541
  2. B
    3521
  3. C
    2154
  4. D
    1545 

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    Solution:

    Let the number of spherical projectiles that can be made from a 44 cm cube of lead be n.
    Now we find the value of the volume of spherical bullets with a diameter of 4 cm and a radius of 2 cm.
    Volume of spherical bullets  = 4 3 π r 3  
    Volume of spherical bullets = = 4 3 π (2) 3  
    = 4 3 π×8c m 3  
    = 4 3 × 22 7 ×8c m 3 =33.52c m 3  
    So to calculate the volume of n number of spherical bullets of radius  2cm   we will multiply it with n.
    Volume of number of spherical bullets =n×33.52c m 3 ......(1)  
    Now, calculate the value of volume of cube of sides
    44cm= (44cm) 3 =85184c m 3 .......(2)  
    Now, equating equation (1) with equation (2) we get;
      85184c m 3 =n×33.52c m 3  
    Now, dividing 85184 by 33.52 we get;
    n= 85184c m 3 33.52c m 3 =2541.2882541  
    So the required number of spherical bullets that can be made out of a cube of metal is 2541.
    So, the correct answer is Option 1.
     
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