posted by Ben
A cylinder fish tank has a volume of 301.44, a rectangular fish tank as a volume of 300, and a triangular prism tank has a volume of 253.75. Obviously the cylinder tank holds more water, but is there a mathematical reason why other than its bigger?
I think you are leaving something out. I assume they all have the same height.
The area of a polygon increases with the number of sides, if the perimeter is constant.
A square has more area than a triangle, and has the most area of any rectangle. A circle has the maximum area for a given perimeter.
The triangular prism has a height of 17.5 in and a base area of 14.5 in. The rectangular prism has dimensions of 10 x 5 x 6, and the cylinder has a height of 6 in and a dimater of 8 in.
given the various dimensions, I'd say it holds more water because it is bigger.
Of course, that is always true :-) ...