Answer:
about 10.24 ft
Explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . where h is the height and r is the radius
The formula for the volume of a sphere is ...
V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r
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We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.
Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...
22,500 ft³ = πr²·(20/3)r = (20π/3)r³
Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...
r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft
The radius of the silo should be about 10.24 feet.