Question

A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone of base radius 8 cm. The height of the cone is

Options

• 12 cm

• 14 cm

• 15 cm

• 18 cm

• 3 . 5 cm

Answer 1

External diameter = 8 cm

Internal diameter = 4 cm

Let the external and internal radii of the hollow metallic sphere be R and r, respectively.

Then,

External radius `8/2 = 4  "cm"`

Internal Radius = `4/2 = 2  "cm"`

Then, volume of the hollow sphere:

`4/3pi[("R")^3 - ("r")^3]`

`= 4/3 pi [(4)^3 - (2)^3]`

Therefore,

Volume of the hollow sphere

`4/3pi[(4)^3 - (2)^3] = 1/3pixx(8)^2 xx "h"`

`=> 4 (64-8) = 64 × "h" `

`=> 224 = 64 × "h" `

`=> "h" = 224/64`

⇒  h = 3.5 cm