The volume, to the nearest cubic inch, of the tower is 2,347.
Brandon made a model of a tower, as shown in the figure. The tower is composed of a square prism and a square pyramid. The height of the pyramid is 2 inches. The height of the prism is 3 feet = 36 inches and the base of the prism is 8 inches long. Let the volumes of the tower, prism, and pyramid be represented by the variables V, V1, and V2.
V1 = L*B*H
V1 = 8*8*36
V1 = 2,304
The volume of the square prism is 2,304 cubic inches.
V2 = (1/3)a²h
V2 = (1/3)(8)²(2)
V2 = 42.67
The volume of the square pyramid is 42.67 cubic inches.
The volume of the tower is the sum of the volumes of the square prism and the square pyramid.
V = V1 + V2
V = 2,304 + 42.67
V = 2,346.67
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