Answer
$3\ ft$
Work Step by Step
Step 1. The volume of the cylinder is $V_1=12\pi x^2$
Step 2. The volume of the two half spheres is $V_2=\frac{4}{3}\pi x^3$
Step 3. The total volume is $\frac{4}{3}\pi x^3+12\pi x^2=144\pi$ or $x^3+9x^2-108=0$
Step 4. Graphically solve the above as shown in the figure to get $x=3\ ft$
