Question

A metallic solid right circular cone is of height 84 cm and the radius of its base is 21 cm. It is melted and recast into a solid sphere. Find the
diameter of the sphere.

Answer 1

We have, 

Height of the cone, h = 84 cm and 

Base radius of the cone, r = 21 cm

Let the radius of the solid sphere be R.

Now,

Volume of the solid sphere = Volume of the solid cone

`=> 4/3pi"R"^3 = 1/3pi"r"^2"h"`

`=> "R"^3 = ("r"^2"h")/4`

`=> "R"^3 = (21xx21xx84)/4`

`=>"R"^3 = 21xx21xx21`

`=>"R" = 21  "cm"`

∴ So, the diameter of the solid sphere is 42 cm.