What would the dimensions of the hexagonal base be?

Question

A farmer plans to build a regular hexagonal corn crib with sides 8 feet high.  If he wants the crib to hold up to 1,000 bushels of corn, what would the dimensions of the hexagonal base be? (1,000 bushels = 1,590 cubic ft.)

Answer 1

The Area of a hexagon is given by the formula Area = (3√3 s²) / 2 where s = length of one side

 

The volume of solid hexagon is given by the formula Volume = h A

where h = height

 

In this case, V = 1,590ft³, so our formula becomes

1,590ft³ = 8ft A, which gives an Area of 198.75ft²

 

then, 198.75ft₂ = (3√3 s²) / 2  We can then solve for s

 

we multiply both sides by 2 to get 397.5ft² = 3√3 s²

 

then 397.5ft² / 3√3 = s², which gives 76ft² = s²

 

finally s = 8.7ft