Question

A solid metallic sphere of diameter 21 cm is melted and recast into small cones of diameter 3.5 cm and height 3 cm each. Find the number of cones so formed.

Answer 1

Radius of sphere`=21/2 "cm"`

Volume of the metallic sphere`=4/3 pir^3`

`=(4/3pixx21/2xx21/2xx21/2)"cm"^3`

Radius of cone `= 3.5/2 "cm"`

Height of cone = 3 cn

Volume of each small cone`=1/3pi"r"^2"h"`

`=(4/3pixx21/2xx21/2xx21/2)"cm"^3`

Radius of cone`=3.5/2  "cm"`

Height of cone = 3 cm

Volume of each small cone`=1/3pi"r"^2"h"` 

`=(1/3pixx35/20xx35/20xx3)"cm"^3`

Number of cones `=("Volume of the metallic sphere")/("Volume of each cone")`

 

`=(4xxpixx21xx21xx3xx20xx20)/(3xx2xx2xx2xxpixx35xx3xx3xx3)`

= 504