{"id":3471,"date":"2024-06-24T16:54:59","date_gmt":"2024-06-24T16:54:59","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3471"},"modified":"2024-08-05T03:00:43","modified_gmt":"2024-08-05T03:00:43","slug":"volumes-of-revolution-cylindrical-shells-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/chapter\/volumes-of-revolution-cylindrical-shells-apply-it\/","title":{"raw":"Volumes of Revolution: Cylindrical Shells: Apply It","rendered":"Volumes of Revolution: Cylindrical Shells: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Determine the volume of a solid formed by rotating a region around an axis using cylindrical shells<\/li>\r\n\t<li>Evaluate the benefits and limitations of different methods (disk, washer, cylindrical shells) for calculating volumes<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Volumes of Revolution<\/h2>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/FJbzYl_trm0?si=beV5AwEREcht-j1V\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/PdOkVlAGtGE?si=mYLU2287N9MxfLD4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/D5NOQa6utCw?si=cdH5j-Nbw31XbDeW\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/aKbyZWGWgYA?si=3BK0qxiURSx4m2ps\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/fap2H4Khico?si=3xb8irU7OAXP5J3K\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\r\n<\/section>\r\n<p>&nbsp;<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Determine the volume of a solid formed by rotating a region around an axis using cylindrical shells<\/li>\n<li>Evaluate the benefits and limitations of different methods (disk, washer, cylindrical shells) for calculating volumes<\/li>\n<\/ul>\n<\/section>\n<h2>Volumes of Revolution<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/FJbzYl_trm0?si=beV5AwEREcht-j1V\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/PdOkVlAGtGE?si=mYLU2287N9MxfLD4\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/D5NOQa6utCw?si=cdH5j-Nbw31XbDeW\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/aKbyZWGWgYA?si=3BK0qxiURSx4m2ps\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/fap2H4Khico?si=3xb8irU7OAXP5J3K\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n<p>&nbsp;<\/p>\n","protected":false},"author":15,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":407,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3471"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":2,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3471\/revisions"}],"predecessor-version":[{"id":4029,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3471\/revisions\/4029"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/407"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3471\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3471"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3471"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3471"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}