Answer
Height of the structure is $18ft$
Work Step by Step
We know the total volume, that is $1400\pi ft^3$. It is sum of volume of the cone and the cylinder.
(Note, height of only cylinder is $\frac{2}{3}h$)
$V_{cylinder}=\pi r^2 h = \frac{200\pi h}{3}$
$V_{cone}=\frac{\pi r^2 h}{3}=\frac{100\pi \frac{1}{3}h}{3}=\frac{100\pi h}{9}$
$\frac{200\pi h}{3}+\frac{100\pi h}{9} = 1400\pi$
$600\pi h + 100\pi h =12600\pi$
$700\pi h = 12600\pi$
$h=\frac{12600\pi}{700\pi}=18ft$
