Exercise 6.1.54
Calculate the volume $V$ and the location of the centroid ($X_c$, $Y_c$, $Z_c$) of the volume shown below. If the volume is made of concrete, what is its weight $W$?
Assume $h = 7.0$ ft, $a_1 = 5.0$ ft, $b_1 = 8.0$ ft, $a_2 = 4.0$ ft, $b_2 = 0.9$ ft, $a_3 = 1.1$ ft, $b_3 = 2.2$ ft. Material is homogeneous with a constant density, $\rho = 149.82$ lb/ft$^3$.
$V = $ ______ ft$^3$
$W = $ ______ lb
$X_c = $ ______ ft
$Y_c = $ ______ ft