By melting a solid cylindrical metal, a few conical materials are to be made. If three times the radius of the cone is equal to twice the radius of the cylinder an the ratio of the height of the cylinder and the height of the cone is 4 : 3, find the number of cones which can be made.
Let R be the radius and H be the height of the cylinder and let r and h be the radius and height of the cone respectively. Then,
3r = 2R
and H ; h = 4 : 3 ....(i)
⇒ 3H = 4h ....(ii)
Let n be the required number of cones which can be made from the materials of the cylinder. Then, the volume of the cylinder will be equal to the sum of the volumes of n cones. Hence, we have
⇒ 3R2H = nr2h
⇒ [From (i) and (ii), R= and H = ]
Hence, the required number of cones is 9. Ans.