Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Solve a composite-volume problem
Problem
Find the volume of this composite solid: a cylinder with \(\text{radius}~3\) and \(\text{height}~10\), with a cone of \(\text{radius}~3\) and \(\text{height}~4\) removed.
The first decision in a composite solid is whether a piece is attached or removed. We’ll represent the cavity with subtraction, calculate the full cylinder and cone separately using their own heights, preserve the cone’s fractional factor, combine like exact terms, and check that the remaining volume is smaller than the original whole.
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