Question

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder. We need to find the ratio of the volume of remaining wood to the volume of the cone hollowed out is ______.

Options

• 1:1

• 1:3

• 2:1

• 3:1

Answer 1

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder. We need to find the ratio of the volume of remaining wood to the volume of the cone hollowed out is 2:1.

Explanation:

The volume of a cylinder is V cylinder = πr²h.

The volume of the largest cone that can be hollowed out (having the same base radius and height) is `V"con" = 1/3 πr^2h`.

The remaining volume after removing the cone.

`"Vermaining" = πr^2h − 1/3 πr^2h = 2/3 πr^2h`

Ratio of remaining wood to the hollowed cone

`"Vremaining"/"Vcone" =(2/3 pir^2h)/(1/3 pir^2h)`

= 2:1