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2 answers:
The answer is 2712.96 but you have to round so it's 2713.
The radius of the cylinder's base is 8, so the volume of the cylinder is

(using the approximation of

).
The sphere has radius 6, so the volume of the sphere is

.
The volume of the shaded region is the difference between the two: 3617.28 - 904.32 = 2712.96. Rounded to the nearest integer gives an answer of 2713.
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