A solid lies between planes perpendicular to the $x$ -axis at $x=0$ and $x=12 .$ The cross-sections by planes perpendicular to the $x$ -axis are circular disks whose diameters run from the line $y=x / 2$ to the line $y=x$ as shown in the accompanying figure. Explain why the solid has the same volume as a right circular cone with base radius 3 and height 12 (FIGURE CAN'T COPY)
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Cavalieri's principle $A$ solid lies between planes perpendicular to the $x$ -axis at $x=0$ and $x=12$ . The cross-sections by planes perpendicular to the $x$ -axis are circular disks whose diameters run from the line $y=x / 2$ to the line $y=x$ as shown in the accompanying figure. Explain why the solid has the same volume as a right circular cone with base radius 3 and height $12 .$
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