{"id":534,"date":"2025-10-09T15:18:36","date_gmt":"2025-10-09T15:18:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=534"},"modified":"2025-12-05T08:37:14","modified_gmt":"2025-12-05T08:37:14","slug":"alternative-coordinate-systems-and-surfaces-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus3\/chapter\/alternative-coordinate-systems-and-surfaces-apply-it\/","title":{"raw":"Alternative Coordinate Systems and Surfaces: Apply It","rendered":"Alternative Coordinate Systems and Surfaces: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Switch between cylindrical and rectangular coordinates<\/li>\r\n \t<li>Switch between spherical and rectangular coordinates<\/li>\r\n \t<li>Recognize and describe different types of quadric surfaces<\/li>\r\n \t<li>Analyze 3D surfaces by looking at their cross-sections and traces<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Rainwater Collection System Design<\/h2>\r\nYou're part of a team redesigning the rainwater collection system for a local community center. The current system uses a large cylindrical storage tank and a dome-shaped overflow reservoir. Your job is to analyze the coordinate systems and surface equations that describe these structures to ensure the new design will work efficiently. 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The current system uses a large cylindrical storage tank and a dome-shaped overflow reservoir. Your job is to analyze the coordinate systems and surface equations that describe these structures to ensure the new design will work efficiently. The engineering team has provided you with various equations and measurements, and you need to convert between coordinate systems and identify the shapes involved.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316606\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316606&theme=lumen&iframe_resize_id=ohm316606&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316612\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316612&theme=lumen&iframe_resize_id=ohm316612&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316613\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316613&theme=lumen&iframe_resize_id=ohm316613&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316614\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316614&theme=lumen&iframe_resize_id=ohm316614&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"font-claude-response-body whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm316615\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316615&theme=lumen&iframe_resize_id=ohm316615&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-534","chapter","type-chapter","status-publish","hentry"],"part":422,"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\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/534","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":9,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/534\/revisions"}],"predecessor-version":[{"id":2761,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/534\/revisions\/2761"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/422"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/534\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=534"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=534"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=534"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}