MathematicsA toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 7 cm and the total height of the toy is 14.5cm. Find the volume of the toy.

A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 7 cm and the total height of the toy is 14.5cm. Find the volume of the toy.


  1. A
    331cm3
  2. B
    449cm3
  3. C
    240cm3
  4. D
    231cm3 

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    Solution:

    Given, diameter of base of conical portion and hemisphere= 7 cm.
    Total height of toy = 14.5cm.
    Radius of base of conical portion and hemisphere = 3.5cm.
     Volume of cone = V= 1 3 π r 2 h   Volume of hemisphere = V = 2 3 π r 3 .  
    Height of the conical portion = Total height – radius of conical portion
    = 14.53.5=11  cm.
     Volume of cone = V= 1 3 ×3.14×3.5×3.5×11  .
    V=141.04c m 3  .
    Volume of hemisphere = V = 2 3 ×3.14×3.5×3.5×3.5  .
    V =89.75c m 3  .
    Volume of toy = volume of conical portion + volume of hemisphere V+ V =141.04+89.75   =231c m 3  .
    Therefore, volume of toy is 231c m 3 .  
    Therefore, option 4 is correct.
     
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