I am trying to generate a solid of known cross sections to be semi-circles for the cardioid $r = 1 + \sin\theta$. I figured that I would need to calculate the volume of individual wedges and sum all of them. My thought was that I needed to use shell method and multiply by $\frac{d\theta}{2\pi}$ in order to get the minuscule volume associated with $d\theta$. I was wondering if anyone could help me correctly employ the shell method in order to obtain the correct equation that would generate the correct volume. I've searched online and the solution is nowhere to be found so this could be a great opportunity to discover something new.
2026-02-23 02:58:31.1771815511
Volume of a polar solid of known cross section
352 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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