Answer:
The radius of the silo should be [tex]16\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the grain silo is equal to the volume of the cylinder plus the volume of a hemisphere
[tex]V=\pi r^{2} h+\frac{4}{6}\pi r^{3}[/tex]
we have
[tex]V=35,500\pi\ ft^{3}[/tex]
[tex]h=4D=8r[/tex]
substitute the values and solve for r
[tex]35,500\pi=\pi r^{2} (8r)+\frac{4}{6}\pi r^{3}[/tex]
Simplify
[tex]35,500=r^{2} (8r)+\frac{4}{6}r^{3}[/tex]
[tex]35,500=8r^{3}+\frac{2}{3}r^{3}[/tex]
[tex]35,500=\frac{26}{3}r^{3}[/tex]
[tex]r^{3}=35,500*(3)/26[/tex]
[tex]r=16\ ft[/tex]
