Q39 of 227 Page 914

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter and height 3 cm. Find the number of cones so formed.

Explanation: Here the volume of all the resulting cones will be exactly equal to the volume of the sphere from which they are formed. Son we would find the volume of sphere and then divide the volume of sphere with the volume of one cone to find the number of cones formed.


Diameter of the sphere = D = 28 cm


Radius of the sphere = 28/2


Radius of the sphere = R = 14 cm
Volume of the sphere(put the value of R)


⇒Volume of the sphere




Let the number of cones formed out of the sphere be ‘x’


Diameter of each cone


Given the height of each cone = h = 3 cm


Then, radius








Volume of ‘n’ number of cones = n × volume of one cone


Volumes of ‘m’ number of cones = volume of sphere





⇒ m = 224 × 3


∴ m = 672


The number of cones formed out of the sphere is 672


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