The radius of a solid metallic sphere is r and the base radius of a solid metallic cone is also r.The vertical height of the cone is 5r.The two solids are melted together and reast into solid right circular cone with base radius 2r.Prove that the height of the cone is 9/4r?

Asked by ADITHYA V | 16th Jan, 2014, 10:16: PM

Expert Answer:

The volume of the cone with radius 'r' and height '5r' cubic units
The volume of the metallic sphere with radius 'r' cubic units
Thus the total volume of the solid when melted ....(1)
 
Given that the radius of the new cone is '2r'.
 
Let 'h' be the height of the new cone.
 
Thus the volume of the new cone
From (1), we have,
 

Answered by Vimala Ramamurthy | 17th Jan, 2014, 10:26: AM

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