{"id":440,"date":"2025-02-13T19:44:56","date_gmt":"2025-02-13T19:44:56","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/volumes-of-revolution-cylindrical-shells-apply-it\/"},"modified":"2025-02-13T19:44:56","modified_gmt":"2025-02-13T19:44:56","slug":"volumes-of-revolution-cylindrical-shells-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/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":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Determine the volume of a solid formed by rotating a region around an axis using cylindrical shells<\/li>\n\t<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 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>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\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>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\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>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\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>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\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>\n<\/section>\n<p>&nbsp;<\/p>\n","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":6,"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":421,"module-header":"","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\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/440"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/440\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/421"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/440\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=440"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=440"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=440"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}