13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.

Page 1 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/1.jpg' width='140' height='200' /> 13.6 Triple Integrals and Applications

Use a triple integral to find volume of a solid region

Find the center of mass and moments of inertia of a solid region

Page 2 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/2.jpg' width='140' height='200' /> Page 3 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/3.jpg' width='140' height='200' /> Page 4 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/4.jpg' width='140' height='200' /> Page 5 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/5.jpg' width='140' height='200' /> Skip, if no time

Page 6 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/6.jpg' width='140' height='200' /> Page 7 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/7.jpg' width='140' height='200' /> Page 8 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=8' data-page='8' class='cut-thumb lazyload' alt='Page 8: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/8.jpg' width='140' height='200' /> Page 9 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=9' data-page='9' class='cut-thumb lazyload' alt='Page 9: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/9.jpg' width='140' height='200' /> Just set up integral. DO NOT SOLVE!

Page 10 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=10' data-page='10' class='cut-thumb lazyload' alt='Page 10: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/10.jpg' width='140' height='200' /> Page 11 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=11' data-page='11' class='cut-thumb lazyload' alt='Page 11: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/11.jpg' width='140' height='200' /> Page 12 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=12' data-page='12' class='cut-thumb lazyload' alt='Page 12: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/12.jpg' width='140' height='200' /> Page 13 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=13' data-page='13' class='cut-thumb lazyload' alt='Page 13: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/13.jpg' width='140' height='200' /> Page 14 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=14' data-page='14' class='cut-thumb lazyload' alt='Page 14: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/14.jpg' width='140' height='200' /> Page 15 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=15' data-page='15' class='cut-thumb lazyload' alt='Page 15: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/15.jpg' width='140' height='200' /> Find the moment of inertia about the z-axis from the previous problem.

Page 16 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=16' data-page='16' class='cut-thumb lazyload' alt='Page 16: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/16.jpg' width='140' height='200' /> Other uses of triple integrals that your book does not go into…

• Density in terms of electrostatics (charge densities

• Potential energy due to the gravitational attraction between two point masses

Page 17 <img data-url='document/136-triple-integrals-and-applications-use-a-triple-integral-to-find-volume.html?page=17' data-page='17' class='cut-thumb lazyload' alt='Page 17: 13.6 Triple Integrals and Applications Use a triple integral to find volume of a solid region Find the center of mass and moments of inertia of a solid.' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader036.cupdf.com/reader036/viewer/2022062421/56649f435503460f94c636c9/html5/thumbnails/17.jpg' width='140' height='200' /> PG. 986 #1-5 ODD, 13, 17, 21, 23, 31Homework