Question

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

Answer 1

The radius of sphere r = 10.5 cm

The volume of sphere

= `4/3 πr^3`

= `4/3 π xx (10.5)^3`

= `4/3 π (21/2)^3`

= `4/3 π (441 xx 21)/8`

= `(144 xx 21)/6 π (cm)^3`

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

Then, volume of sphere = n × volume of cone

`(441 xx 21)/6 π = n xx 1/3 xx π 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)`

n = 126

Hence, the no. of cones = 126.