Find the volume of the biggest cone that can fit inside a cube of side 3 cm.


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Answer:

 

9π
4
  cm3

Step by Step Explanation:
  1. The volume of a cone is of radius r and height h =  
    1
    3
     πr2h.
  2. Since we have to fit it inside a cube of side 3 cm, we see that the diameter of the cone will be 3 cm, and the height will be 3 cm (A cone larger than this in diameter or height will not fit inside the cube).
  3. So, the radius of this cone =  
    3
    2
      cm = 1.5 cm
  4. Putting these values into the equation of the volume, we get the volume of the cone =  
    1
    3
      × π × ( 
    3
    2
     )2 × 3 cm3
  5. On solving, we get the volume of the cone =  
    9π
    4
      cm3

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