Problem 37 A factory chimney is in the form of frustum of regular square pyramid. The chimney is 125 ft. high the edges of its bases are 12 ft. and 8 ft., respectively. The cross-section of the flue is 6 ft. square. How many cubic feet of material does the chimney contain?

Solution 37

$V = \frac{1}{3}(A_1 + A_2 + \sqrt{A_1 \, A_2}) \, h - A_b h$

$V = \frac{1}{3}(12^2 + 8^2 + \sqrt{12^2 \cdot 8^2}) \, (125) - 6^2(125)$

$V = 8166.67 ~ \text{ft.}^3$ answer

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