Question

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

Explanation:

Volume of remaining wood = `"V"_"Cylinder" - "V"_"Cone"`

= `pir^2h - 1/3pir^2h`

= `2/3pir^2h`

Volume of hollowed out = `1/3pir^2h`

Required Ratio = `(2/3pir^2h)/(1/3pir^2h)`

= `2/3 xx 3/1`

= `2/1`

= 2 : 1