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Below is the solution:
<span>sweeping the triangular end thru the length:
V = (1/2) (8ft) (7ft) (12ft)
V = </span><span>328 ft3 </span>
Use distributive property
4y^2 + 6y^3 - 3y^2 + y^3
combine like terms
y^2 + 7y^3
Hmmmmmmmmmmmmmmmmmmmmmmmmmmm
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.