Q7 of 67 Page 195

How many cones of radius 3 cm and height 6 cm can be made by melting a metallic sphere of radius 9 cm.

base radius of cone= rc = 3 cm


Height of cone = h = 6 cm


Radius of sphere = rs = 9 cm


volume of cone = πrc2h


Volume of sphere = πrs3


Let n be the number of cones made


As the sphere is melted and then the cones are made from the same amount of melted sphere therefore the volume remains same


i.e. volume of n cones made = volume of sphere


⇒ n × πrc2h = πrs3


⇒ nrc2h = 4rs3


Substituting values


⇒ n × 32 × 6 = 4 × 93


⇒ n × 6 = 4 × 9 × 9


⇒ n = 6 × 9


⇒ n = 54


Number of cones formed = 54


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