Answer:
[tex]r=16\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere
so
[tex]V=\pi r^{2}h+\frac{4}{6}\pi r^{3}[/tex]
In this problem we have
[tex]V=35,500\pi\ ft^{3}[/tex]
[tex]h=4D=8r[/tex] ----> 4 times the diameter is equal to 8 times the radius
substitute in the formula and solve for r
[tex]35,500\pi=\pi r^{2}(8r)+\frac{4}{6}\pi r^{3}[/tex]
Simplify pi
[tex]35,500=8r^{3}+\frac{4}{6}r^{3}[/tex]
[tex]35,500=r^{3}[8+\frac{4}{6}][/tex]
[tex]35,500=r^{3}[\frac{52}{6}][/tex]
[tex]r^{3}=35,500/[\frac{52}{6}][/tex]
[tex]r=16\ ft[/tex]
