Answer:
He should refute the affirmation, because the volumes are different.
Step-by-step explanation:
The area of a regular hexagon is given by the equation:
[tex]Area = 3\sqrt{3}side^2/2[/tex]
And the volume is given by:
[tex]Volume = Area * height[/tex]
The volume of the internal hexagon hole is given by:
[tex]V_{internal} = (3\sqrt{3}*4^2/2) * 2[/tex]
[tex]V_{internal} = 83.1384\ cm^3[/tex]
The volume of the ring is given by the volume of the bigger hexagon minus the volume of the internal hexagon:
[tex]V_{ring} = V_{external} - V_{internal}[/tex]
[tex]V_{ring} = (3\sqrt{3}*6^2/2) * 2 - 83.1384[/tex]
[tex]V_{ring} = 187.0615 - 83.1384[/tex]
[tex]V_{ring} = 103.9231\ cm^3[/tex]
The volumes are different, so the assistant should refute Dakota.
