Mathematical Modeling Questions for Secondary School Curriculum | Page 12

AQUARIUM DESIGN

Author : Mihaela Git
A manufacturer is designing an aquarium whose base is a regular hexagon .
The aquarium should have a volume of 24 cubic feet and use the least amount of material possible . Let l be the length ( in feet ) of a side of the base , and let h be the height ( in feet ).
1 .
Write an equation that gives h in terms of l .
2 .
Determine the function that expresses the surface of the aquarium
depending on the side of the base .
3 .
Use the GeoGebra program to graphically represent this function .
4 .
Find the dimensions s and h that minimize the amount of material used .
5 .
For l and h determined at 4 ., how many liters of water must be put in the
aquarium for the water to wet three quarters of the edge of the aquarium ?
Related Topics and Concepts : Geometry , Functions Real Life Context : Construction engineering