Question

A hollow sphere of external and internal diameters 8 cm and 4 cm, respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone. 

Answer 1

We have,

External radius of the hollow sphere, `"R"1 = 8/2 =4  "cm"`

Internal radius of the hollow sphere, `"R"2 = 4/2 = 2  "cm" and`

Let the height of the cone, `r = 8/2 = 4  "cm"`

Let the height of the cone be h.

Now, Volume of the cone = Volume of the hollow sphere 

`=> 1/3pi"r"^2"h" = 4/3pi"R"_1^3 - 4/3pi"R"_2^3`

`=> 1/3pi"r"^2"h" = 4/3pi("R"_1^3 - "R"_2^3)`

`=> "h" = 4/"r"^2 ("R"_1^3 - "R"_2^3)`

`=> "h" = 4/(4xx4) (4^3 - 2^3)`

`=>"h" = 1/4(64-8)`

`=> "h" = 1/4xx56`

∴ h = 14 cm

So, the height of the cone is 14 cm.