Question

A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm.Find the number of cones so formed. 

Answer 1

Let the number of cones formed be n.

Given: Radius of sphere, r = 10.5 cm

Volume of sphere`V_1=pi_3^4-r^3`

`rArrV rpi_3^4-(10.5)cm^3`

Given: Height of cone, h = 3 cm and radius of cone, R = 3.5 cm

`therefore` Volume of each smaller come `v_2=1/3piR^2h`

`rArr V_2=1/3pi(3.5)^2xx3cm^3`

Since the solid sphere is melted and recast into smaller cones,

n × Volume of each smaller cone = Volume of the sphere

`thereforenxx1/3 pi (3.5)^2xx3=4/3pi(10.5)^3`

`rArrn=(4xx(10.5)^3)/((3.5)^2xx3)`

`rArrn=126`

Thus, the number of smaller cones formed is 126.