Q9 of 67 Page 195

Find the number of cones of radius 3 cm and height 6 cm that can be made by melting a metallic sphere of radius 9 cm.

Radius of metal sphere = rs = 9 cm


Radius of cone formed = rc = 3 cm


Height of cone = h = 6 cm


The sphere is melted and the volume of sphere is used to make cones


Volume of sphere = πrs3


Volume of cone = πrc2h


Let n cones are made then the volume of n cones is same as the volume of sphere


⇒ πrs3 = n × πrc2h


⇒ 4rs3 = nrc2h


Substitute values


⇒ 4 × 93 = n × 32 × 6


⇒ 4 × 92 = n × 6


⇒ 4 × 92 = 6n


⇒ 324 = 6n


⇒ n = 54


Therefore, 54 cones are made


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