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Volume of a Right Circular Cone

Slant height l = units

Volume of a cone =
pr2h cu. units
 

Example

A hollow sphere of internal and external diameters of 4 cm and 8 cm respectively, is melted into a cone of base diameter 8 cm. Find the height of the cone.
 

Solution

Inner radius of the sphere = 2 cm.

External radius of the sphere = 4 cm

Volume of the metal of the sphere

        = volume of the external sphere - Volume of the internal sphere

        = 
pR3 - pr3   
                         
          
        =
p (R3 - r3) cm3

Þ   V = ´ (43 - 23)

         =
´ ´ 56 cm3
Volume of the cone = Volume of the metal


Þ        pr2 h = ´ p ´ 56

Þ        ´ (4)2 ´ h = ´ 56

Þ         h = 14 cm

hence, height of the cone
= 14 cm
 


 

Volume of a Right Circular Cone

 




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