020 Review Problem - Volume of a factory chimney

Volume of frustum
$V_f = \frac{1}{3}(A_1 + A_2 + \sqrt{A_1A_2})h$

$V_f = \frac{1}{3}[ \, 16^2 + 10^2 + \sqrt{16^2(10^2)} \, ](180)$

$V_f = 30\,960 ~ \text{ft.}^3$
 

Volume of flue (parallelepiped)
$V_p = A_bh = 7^2(180)$

$V_p = 8\,820 ~ \text{ft.}^3$
 

Volume of chimney
$V = V_f - V_p = 30960 - 8820$

$V = 22\,140 ~ \text{ft.}^3$           answer