Question

To test his assistant, noted adventurer Dakota Davis states that the volume of the regular hexagonal ring at right is equal to the volume of the regular hexagonal hole in its center. The assistant must confirm or refute this, using dimensions shown in the figure. What should he say to Dakota?

Answer 1

He should refute the affirmation, because the volumes are different.

Explanation:

The area of a regular hexagon is given by the equation:

`Area = 3√(3)side^2/2`

And the volume is given by:

`Volume = Area * height`

The volume of the internal hexagon hole is given by:

`V_(internal) = (3√(3)*4^2/2) * 2`

`V_(internal) = 83.1384\ cm^3`

The volume of the ring is given by the volume of the bigger hexagon minus the volume of the internal hexagon:

`V_(ring) = V_(external) - V_(internal)`

`V_(ring) = (3√(3)*6^2/2) * 2 - 83.1384`

`V_(ring) = 187.0615 - 83.1384`

`V_(ring) = 103.9231\ cm^3`

The volumes are different, so the assistant should refute Dakota.