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A math quiz question from math 234, dated november 7, 2007. The question asks students to find the moment of inertia of a solid with given boundaries and mass density. The solid is bounded above by a hyperboloid and below by a cone. Students are required to write the iterated integral for the moment of inertia and then compute the integral.
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A solid is bounded above by the hyperboloid z =
√ x^2 + y^2 + 1 and below by the cone z =
√ 2(x^2 + y^2 ). The mass density δ(x, y, z) = z. (a) Write the moment of inertia Iz =
∫ ∫ ∫ (x^2 + y^2 )δ(x, y, z) dV as an ap- propriate iterated integral.
(b) Compute the integral.
