If a cone is cut by a plane parallel to its base, the portion of a solid between this plane and the base is known as frustum of a cone.

            The volume denoted by ABCD in figure is a frustum of the cone ABE.

Volume of Frustum of a Cone:
            Since, we know that cone is a limit of a pyramid therefore; frustum of a cone will be the limit of frustum of a pyramid. But volume of a pyramid is
                       
Where             
                       
                   
                       

Example:
            A cone 12cm high is cut 8cm from the vertex to form a frustum with a volume of 190cu.cm. Find the radius of the cone.

Solution:
            Given that:
            Height of cone
            Height of frustum         
            Volume of frustum       

            Now volume of frustum cone
                       
            or        
            or        
                       

            Hence required radius of cone

Curved Surface Area of a Frustum of a Cone:
            Since, a cone is the limiting case of a pyramid, therefore the lateral surface of frustum of a cone can be deduced from the slant surface of frustum of a pyramid, i.e., curved (lateral) surface of frustum of cone.

           
           
            , being the slant height of frustum,  and  being two radius of bases.

Note:
            (1)        Total surface area of frustum of a cone
                                    
            (2)        To find the slant height of the cone, use Pythagorean theorem.

Example:
            A material handling bucket is in the shape of the frustum of a right circular cone as shown in figure. Find the volume and the total surface area of the bucket.

Solution:

            Slant height                  
            Lateral surface area     
                                                                                    
        Base areas                   
                                                   
        Total surface area    
                              
                     

            Volume