Question

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

Answer 1

The radius of sphere r = 10.5 cm

The volume of sphere

`= 4/3 pi x^3`

`= 4/3 pi xx (10. 5)^3`

`= 4/3 pi (21/2)^3`

`= 4/3 pi (441 xx 21)/8`

`=(144 xx 21)/6 pi (cm)^3`

Let n be the number of cones obtained when the sphere is recast in to small cones, each of radius 3.5 and height 3 cm.

Then, volume of sphere = n × volume of cone

`(441 xx 21)/6 pi = n xx 1/3 xx pi xx (3.5)^2 xx 3`

   `(441 xx 21)/6 = n xx 1/3 xx 7/2 xx 7/2 xx 3`

     `441 xx 21 = (n xx 49 xx 3)/2`

                   `n = (441 xx 21 xx 2 )/(49 xx 3) = 126`

                  `n = 126`

Hence, the no. of cones = 126