The radius of the cylinder's base is 8, so the volume of the cylinder is \(\pi8^218\approx3617.28\) (using the approximation of \(\pi\approx3.14\)).
The sphere has radius 6, so the volume of the sphere is \(\dfrac43\pi6^3\approx904.32\).
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.
