(i) A solid E lies between the paraboloid z = 24 - x² - y² and the cone z = 2√x² + y². Using cylindrical coordinates, find volume of E. (ii) Set up triple integrals to find the centroid of E (i.e., center of mass if the density is a constant).

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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(i) A solid \( E \) lies between the paraboloid \( z = 24 - x^2 - y^2 \) and the cone \( z = 2\sqrt{x^2 + y^2} \). Using cylindrical coordinates, find the volume of \( E \).

(ii) Set up triple integrals to find the centroid of \( E \) (i.e., center of mass if the density is a constant).
Transcribed Image Text:(i) A solid \( E \) lies between the paraboloid \( z = 24 - x^2 - y^2 \) and the cone \( z = 2\sqrt{x^2 + y^2} \). Using cylindrical coordinates, find the volume of \( E \). (ii) Set up triple integrals to find the centroid of \( E \) (i.e., center of mass if the density is a constant).
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