so i have to find the moment of inertia of a solid cone given by the equations z = ar and z = b by using a triple integral. The density of the cone is assumed to be 1. so the integral looks like ∫ ∫ ∫ r^2 dV. so first i did it with dV = rdrdθdz with limits r (from 0 to z/a), θ (from 0 to 2pi), and z (from 0 to b) and i got the answer (pi)b^5 / (10a^4) which seems to be right. now i am trying to do the triple integral instead with dV = rdzdrdθ. i am having trouble deciding the limits now. for z, i know that r and θ are to be kept constant so my limits for z are from ar to b. then my limits for r are from 0 to z/a and my limits for θ are from 0 to 2pi. however after doing the integrations, my answer turned out messy involving a's, b's, and z's which shouldn't be in the final answer. how do i set up the limits correctly when integrating with respect to z first, then r and theta afterwards?(adsbygoogle = window.adsbygoogle || []).push({});

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# Homework Help: Moment of inertia with triple integrals

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