Question

Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?

Answer 1

For a cone to fit perfectly inside the can it needs to have the same base circle size and same height.

Work out the height of the can first:

`height = (volume)/( \pi *radius^(2) )`

`height = (15)/( \pi *1^(2) )`

`height = 4.77`

This means your cone can have a max height of 4.77 and the same base circle (diameter of 2 / radius 1).

Work out the volume of cone:

`Volume = \pi * radius^(2) * (height)/(3)`

`Volume = \pi * 1^(2) * (4.77)/(3)`

`Volume = 5  \pi * radius^(2) * (height)/(3)`

The volume of your cone which fits perfectly inside the can is 5.