A transformation is a rigid motion if it preserves

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

  about 10.24 ft

Step-by-step 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.