# Wall Corner

The wall’s corner sectors were all assumed to have a square base and all be the same size in the calculations. In order to calculate the volume of the corner sectors, each sector was divided into one of four geometric shapes:

Rectangular prism
Square prism
Pyramid
Triangular prism

The volume of the rectangular prisms was calculated by multiplying the height of the fort, H, the depth of the inside of the slope, I, and the length of the flat top, T. (Vol = H*I*T).

The volume of the square prisms were calculated by multiplying the height of the fort, H, by the square of the length of the flat top, T, (Vol = H*T^2).

The volume of the pyramids was calculated by multiplying 1/3 by the height of the fort, H, and the square of the depth of a slope, I, (Vol = (1/3)*H*I^2).

The volume of the triangular prisms was calculated by multiplying (1/2) by the height of the fort, H, the depth of the outside slope, O, and the quantity of the depth of the inside slope, I, plus the length of the flat top, T, (Vol = (1/2)*H*O*(I + T)).

The total volume of the sector is found by adding the volumes of the geometric regions. TotalVolume = (2*RectPrism) + (SquarePrim) + (2*InnerPyramid) + (2*TriangularPrism) + (SmallPyramid)).

Minimum Estimate Maximum Estimate
H (Height of Fort) 5.2 5.5
I (Depth of Inside Slope) 5 5.1
T (Length of Flat Top) 1.8 2.1
O (Depth of outside slope) 2.1 2.3
Rectangular Prisms 46.8 58.905
Square Prism 16.848 24.255
Inner Pyramids 43.33333 47.685
Triangular Prisms 37.128 45.54
Small Pyramid 7.644 9.698333
Volume of sector 1 279.0147 338.2133
Total Volume 1674.088 2029.28