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

Hi Kailes, the volume of a hexagon is given by the equation, V = B * H, where V is the volume, B is the base of the hexagon, and H is the height of the hexagon.

 

The volume of the hexagon is equal to 1590 ft³. The height of the hexagon is equal to 8 feet.

 

Solving for the base of the hexagon:

 

B = V / H

 

B = 1590 / 8

 

B = 198.75 ft²

 

Area of the base of a hexagon:

 

The area of the base of a hexagon is given by the formula:

 

A =((3 * √3) / 2) * a², where a is the length of a side of the hexagon.

 

Substituting and solving for a gives:

 

(198.75 * 2) / (3 * √3) = a²

 

a² ≈ 76.5

 

a ≈ 8.75 feet

 

The dimensions of the hexagonal base would be approximately 8.75 feet on each side.

 

Questions?

Answer 2

The volume of an object is the area of its base times the height.

 

V = A*h

 

We know from the question that the volume is 1590 and the height is 8.

 

1590 = A*8

 

A = 198.75 ft^2

 

A regular hexagon can be thought of as 6 equilateral triangles all fit together. We know the area of an equilateral triangle is 1/2*b*h. The height of one of the equilateral triangles is

 

h = 1/2*b*tan(60)

 

   = 1/2*b*sqrt(3)

 

   = sqrt(3)/2*b

 

A = 1/2*b*(sqrt(3)/2*b)

 

   = sqrt(3)/4*b^2

 

6 of these little triangles will sum up to the area needed.

 

198.75 = 6*sqrt(3)/4*b^2

 

b^2 = ~76.2 ft

 

b = ~8.7 ft.

 

The hexagon will be comprised of 6 equal sides of 8.7ft each.