Chapter 15.6, Problem 22E

BuyFind*arrow_forward*

8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use a triple integral to find the volume of the given solid.

**22**. The solid enclosed by the cylinder *x ^{2} + z^{2} =* 4 and the planes

To determine

**To find:** The volume of the solid enclosed by the cylinder

Explanation

Cylinder and planes intersect each other to form the required solid.

Express the surface of the cylinder

The surface of the cylinder is in the circle form. So, limit of *r* varies from 0 to 2.

From the given planes, *y* varies from

Let *E* be the region enclosed by solid where

The volume of integral for the solid is,

Integrate the given integral with respect to *y* and apply the limit of it.

Integrate the given integral with respect to *r* and apply the limit of it

Sect-15.1 P-1ESect-15.1 P-2ESect-15.1 P-3ESect-15.1 P-4ESect-15.1 P-5ESect-15.1 P-6ESect-15.1 P-7ESect-15.1 P-8ESect-15.1 P-9ESect-15.1 P-10E

Sect-15.1 P-11ESect-15.1 P-12ESect-15.1 P-13ESect-15.1 P-14ESect-15.1 P-15ESect-15.1 P-16ESect-15.1 P-17ESect-15.1 P-18ESect-15.1 P-19ESect-15.1 P-20ESect-15.1 P-21ESect-15.1 P-22ESect-15.1 P-23ESect-15.1 P-24ESect-15.1 P-25ESect-15.1 P-26ESect-15.1 P-27ESect-15.1 P-28ESect-15.1 P-29ESect-15.1 P-30ESect-15.1 P-31ESect-15.1 P-32ESect-15.1 P-33ESect-15.1 P-34ESect-15.1 P-35ESect-15.1 P-36ESect-15.1 P-37ESect-15.1 P-38ESect-15.1 P-39ESect-15.1 P-40ESect-15.1 P-41ESect-15.1 P-42ESect-15.1 P-43ESect-15.1 P-44ESect-15.1 P-47ESect-15.1 P-48ESect-15.1 P-49ESect-15.1 P-50ESect-15.1 P-52ESect-15.2 P-1ESect-15.2 P-2ESect-15.2 P-3ESect-15.2 P-4ESect-15.2 P-5ESect-15.2 P-6ESect-15.2 P-7ESect-15.2 P-8ESect-15.2 P-9ESect-15.2 P-10ESect-15.2 P-11ESect-15.2 P-12ESect-15.2 P-13ESect-15.2 P-14ESect-15.2 P-15ESect-15.2 P-16ESect-15.2 P-17ESect-15.2 P-18ESect-15.2 P-19ESect-15.2 P-20ESect-15.2 P-21ESect-15.2 P-22ESect-15.2 P-23ESect-15.2 P-24ESect-15.2 P-25ESect-15.2 P-26ESect-15.2 P-27ESect-15.2 P-28ESect-15.2 P-29ESect-15.2 P-30ESect-15.2 P-31ESect-15.2 P-32ESect-15.2 P-33ESect-15.2 P-34ESect-15.2 P-35ESect-15.2 P-36ESect-15.2 P-37ESect-15.2 P-38ESect-15.2 P-39ESect-15.2 P-40ESect-15.2 P-45ESect-15.2 P-46ESect-15.2 P-47ESect-15.2 P-48ESect-15.2 P-49ESect-15.2 P-50ESect-15.2 P-51ESect-15.2 P-52ESect-15.2 P-53ESect-15.2 P-54ESect-15.2 P-55ESect-15.2 P-56ESect-15.2 P-57ESect-15.2 P-58ESect-15.2 P-59ESect-15.2 P-60ESect-15.2 P-61ESect-15.2 P-62ESect-15.2 P-63ESect-15.2 P-64ESect-15.2 P-65ESect-15.2 P-66ESect-15.2 P-67ESect-15.2 P-68ESect-15.2 P-69ESect-15.3 P-1ESect-15.3 P-2ESect-15.3 P-3ESect-15.3 P-4ESect-15.3 P-5ESect-15.3 P-6ESect-15.3 P-7ESect-15.3 P-8ESect-15.3 P-9ESect-15.3 P-10ESect-15.3 P-11ESect-15.3 P-12ESect-15.3 P-13ESect-15.3 P-14ESect-15.3 P-15ESect-15.3 P-16ESect-15.3 P-17ESect-15.3 P-18ESect-15.3 P-19ESect-15.3 P-20ESect-15.3 P-21ESect-15.3 P-22ESect-15.3 P-23ESect-15.3 P-24ESect-15.3 P-25ESect-15.3 P-26ESect-15.3 P-27ESect-15.3 P-28ESect-15.3 P-29ESect-15.3 P-30ESect-15.3 P-31ESect-15.3 P-32ESect-15.3 P-33ESect-15.3 P-34ESect-15.3 P-35ESect-15.3 P-36ESect-15.3 P-37ESect-15.3 P-38ESect-15.3 P-39ESect-15.3 P-40ESect-15.3 P-41ESect-15.4 P-1ESect-15.4 P-2ESect-15.4 P-3ESect-15.4 P-4ESect-15.4 P-5ESect-15.4 P-6ESect-15.4 P-7ESect-15.4 P-8ESect-15.4 P-9ESect-15.4 P-10ESect-15.4 P-11ESect-15.4 P-12ESect-15.4 P-13ESect-15.4 P-14ESect-15.4 P-15ESect-15.4 P-16ESect-15.4 P-17ESect-15.4 P-18ESect-15.4 P-19ESect-15.4 P-20ESect-15.4 P-21ESect-15.4 P-22ESect-15.4 P-23ESect-15.4 P-24ESect-15.4 P-27ESect-15.4 P-28ESect-15.4 P-29ESect-15.4 P-30ESect-15.4 P-32ESect-15.4 P-33ESect-15.5 P-1ESect-15.5 P-2ESect-15.5 P-3ESect-15.5 P-4ESect-15.5 P-5ESect-15.5 P-6ESect-15.5 P-7ESect-15.5 P-8ESect-15.5 P-9ESect-15.5 P-10ESect-15.5 P-11ESect-15.5 P-12ESect-15.5 P-13ESect-15.5 P-14ESect-15.5 P-21ESect-15.5 P-22ESect-15.5 P-23ESect-15.5 P-24ESect-15.6 P-1ESect-15.6 P-2ESect-15.6 P-3ESect-15.6 P-4ESect-15.6 P-5ESect-15.6 P-6ESect-15.6 P-7ESect-15.6 P-8ESect-15.6 P-9ESect-15.6 P-10ESect-15.6 P-11ESect-15.6 P-12ESect-15.6 P-13ESect-15.6 P-14ESect-15.6 P-15ESect-15.6 P-16ESect-15.6 P-17ESect-15.6 P-18ESect-15.6 P-19ESect-15.6 P-20ESect-15.6 P-21ESect-15.6 P-22ESect-15.6 P-25ESect-15.6 P-26ESect-15.6 P-27ESect-15.6 P-28ESect-15.6 P-29ESect-15.6 P-30ESect-15.6 P-31ESect-15.6 P-32ESect-15.6 P-33ESect-15.6 P-34ESect-15.6 P-35ESect-15.6 P-36ESect-15.6 P-37ESect-15.6 P-38ESect-15.6 P-39ESect-15.6 P-40ESect-15.6 P-41ESect-15.6 P-42ESect-15.6 P-43ESect-15.6 P-44ESect-15.6 P-45ESect-15.6 P-46ESect-15.6 P-47ESect-15.6 P-48ESect-15.6 P-51ESect-15.6 P-52ESect-15.6 P-53ESect-15.6 P-54ESect-15.7 P-1ESect-15.7 P-2ESect-15.7 P-3ESect-15.7 P-4ESect-15.7 P-5ESect-15.7 P-6ESect-15.7 P-7ESect-15.7 P-8ESect-15.7 P-9ESect-15.7 P-10ESect-15.7 P-11ESect-15.7 P-12ESect-15.7 P-13ESect-15.7 P-14ESect-15.7 P-15ESect-15.7 P-16ESect-15.7 P-17ESect-15.7 P-18ESect-15.7 P-19ESect-15.7 P-20ESect-15.7 P-21ESect-15.7 P-22ESect-15.7 P-23ESect-15.7 P-24ESect-15.7 P-25ESect-15.7 P-26ESect-15.7 P-27ESect-15.7 P-28ESect-15.7 P-29ESect-15.7 P-30ESect-15.7 P-31ESect-15.8 P-1ESect-15.8 P-2ESect-15.8 P-3ESect-15.8 P-4ESect-15.8 P-5ESect-15.8 P-6ESect-15.8 P-7ESect-15.8 P-8ESect-15.8 P-9ESect-15.8 P-10ESect-15.8 P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ESect-15.8 P-22ESect-15.8 P-23ESect-15.8 P-24ESect-15.8 P-25ESect-15.8 P-26ESect-15.8 P-27ESect-15.8 P-28ESect-15.8 P-29ESect-15.8 P-30ESect-15.8 P-31ESect-15.8 P-32ESect-15.8 P-33ESect-15.8 P-34ESect-15.8 P-35ESect-15.8 P-36ESect-15.8 P-37ESect-15.8 P-38ESect-15.8 P-41ESect-15.8 P-42ESect-15.8 P-43ESect-15.8 P-44ESect-15.8 P-45ESect-15.8 P-46ESect-15.8 P-48ESect-15.8 P-49ESect-15.9 P-1ESect-15.9 P-2ESect-15.9 P-3ESect-15.9 P-4ESect-15.9 P-5ESect-15.9 P-6ESect-15.9 P-7ESect-15.9 P-8ESect-15.9 P-9ESect-15.9 P-10ESect-15.9 P-11ESect-15.9 P-12ESect-15.9 P-13ESect-15.9 P-14ESect-15.9 P-15ESect-15.9 P-16ESect-15.9 P-17ESect-15.9 P-18ESect-15.9 P-19ESect-15.9 P-20ESect-15.9 P-21ESect-15.9 P-22ESect-15.9 P-23ESect-15.9 P-24ESect-15.9 P-25ESect-15.9 P-26ESect-15.9 P-27ESect-15.9 P-28ECh-15 P-1RCCCh-15 P-2RCCCh-15 P-3RCCCh-15 P-4RCCCh-15 P-5RCCCh-15 P-6RCCCh-15 P-7RCCCh-15 P-8RCCCh-15 P-9RCCCh-15 P-10RCCCh-15 P-1RQCh-15 P-2RQCh-15 P-3RQCh-15 P-4RQCh-15 P-5RQCh-15 P-6RQCh-15 P-7RQCh-15 P-8RQCh-15 P-9RQCh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-1PCh-15 P-2PCh-15 P-3PCh-15 P-4PCh-15 P-5PCh-15 P-6PCh-15 P-7PCh-15 P-8PCh-15 P-9PCh-15 P-10PCh-15 P-11PCh-15 P-12PCh-15 P-13P

Calculus: Early Transcendental Functions

Calculus: An Applied Approach (MindTap Course List)

Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus

Multivariable Calculus

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Single Variable Calculus

Finite Mathematics

Probability and Statistics for Engineering and the Sciences

Understanding Basic Statistics

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Elementary Technical Mathematics

Mathematical Excursions (MindTap Course List)

Elementary Geometry For College Students, 7e

Contemporary Mathematics for Business & Consumers

Calculus: Early Transcendental Functions (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Study Guide for Stewart's Multivariable Calculus, 8th

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Elementary Geometry for College Students

Finite Mathematics for the Managerial, Life, and Social Sciences