Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Compare two exact solid volumes by relation, ratio, and difference
Problem
Solid A is a cylinder of radius \(3\) and height \(10\); solid B is a cone with the same radius and height. Calculate \(\text{both}~\text{exact}~\text{volumes}\), then state their relation, the simplified ratio \(A:B\), the signed difference \(A~-~B\), and the multiplicative comparison.
Because the solids share a radius and height, their common base-times-height factor makes the formula difference especially visible. We’ll write both exact volumes, keep pi symbolic, preserve the requested A-to-B order, and distinguish a ratio, a signed difference, and a multiplicative comparison rather than blending those measures.
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