{"id":690,"date":"2025-10-09T15:30:32","date_gmt":"2025-10-09T15:30:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=690"},"modified":"2025-12-12T14:27:37","modified_gmt":"2025-12-12T14:27:37","slug":"double-integrals-in-polar-coordinates-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus3\/chapter\/double-integrals-in-polar-coordinates-apply-it\/","title":{"raw":"Double Integrals in Polar Coordinates: Apply It","rendered":"Double Integrals in Polar Coordinates: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Use polar coordinates to evaluate double integrals<\/li>\r\n \t<li>Use double integrals in polar coordinates to calculate areas and volumes<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Calculating Storm Rainfall Using Polar Coordinates<\/h2>\r\nYou volunteer at a local emergency preparedness center during storm season. A storm system is approaching your area, and the weather radar displays precipitation intensity as a function of distance and angle from the radar station located at the center of town. The radar measures rainfall rate in centimeters per hour at each point in the region. Your task is to analyze the radar data to calculate total rainfall amounts over different neighborhoods. This information helps emergency coordinators decide where to position response teams and sandbag supplies. The radar naturally provides data in polar coordinates, with distance [latex]r[\/latex] measured in kilometers from the station and angle [latex]\\theta[\/latex] measured from due east.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]316957[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]316958[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]316959[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]316960[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Use polar coordinates to evaluate double integrals<\/li>\n<li>Use double integrals in polar coordinates to calculate areas and volumes<\/li>\n<\/ul>\n<\/section>\n<h2>Calculating Storm Rainfall Using Polar Coordinates<\/h2>\n<p>You volunteer at a local emergency preparedness center during storm season. A storm system is approaching your area, and the weather radar displays precipitation intensity as a function of distance and angle from the radar station located at the center of town. The radar measures rainfall rate in centimeters per hour at each point in the region. Your task is to analyze the radar data to calculate total rainfall amounts over different neighborhoods. This information helps emergency coordinators decide where to position response teams and sandbag supplies. The radar naturally provides data in polar coordinates, with distance [latex]r[\/latex] measured in kilometers from the station and angle [latex]\\theta[\/latex] measured from due east.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm316957\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316957&theme=lumen&iframe_resize_id=ohm316957&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm316958\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316958&theme=lumen&iframe_resize_id=ohm316958&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm316959\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316959&theme=lumen&iframe_resize_id=ohm316959&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm316960\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=316960&theme=lumen&iframe_resize_id=ohm316960&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/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-690","chapter","type-chapter","status-publish","hentry"],"part":432,"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\/690","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":4,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/690\/revisions"}],"predecessor-version":[{"id":2778,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/690\/revisions\/2778"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/432"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/690\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=690"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=690"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=690"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}