{"id":4504,"date":"2023-06-13T04:13:00","date_gmt":"2023-06-13T04:13:00","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4504"},"modified":"2025-08-26T03:58:07","modified_gmt":"2025-08-26T03:58:07","slug":"volume-and-surface-area-apply-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/volume-and-surface-area-apply-it-1\/","title":{"raw":"Volume and Surface Area: Apply It 1","rendered":"Volume and Surface Area: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Find the volume of a rectangular solid, sphere, cylinder, and cone<\/li>\r\n\t<li>Find the surface area of a rectangular solid, sphere, and cylinder<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Journey into 3D Geometry: Exploring Shapes, Volume, and Surface Area<\/h2>\r\n<p>Welcome to the fascinating world of 3D geometry! Here, we'll explore various three-dimensional shapes such as rectangular solids, spheres, cylinders, and cones. We'll also delve into how to calculate their volume and surface area. These skills are crucial in fields like engineering, architecture, and physics.<\/p>\r\n<center>\r\n[caption id=\"attachment_7081\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-7081\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-300x231.jpg\" alt=\"3D shapes including cubes, trapezoids, spheres, and rectangles.\" width=\"500\" height=\"386\" \/> Figure 1. Knowing the volumes and surface areas for 3D shapes can be useful for the following tasks[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>You're designing a rectangular box for packaging.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9698[\/ohm2_question]<\/section>\r\n<p>Now, let's look at how to calculate the surface area of the rectangular solid.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9699[\/ohm2_question]<\/section>\r\n<p>Next, we'll move onto spherical shapes which are common in astronomy and physics.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9700[\/ohm2_question]<\/section>\r\n<p>Let's consider the surface area of this sphere now.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9701[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Find the volume of a rectangular solid, sphere, cylinder, and cone<\/li>\n<li>Find the surface area of a rectangular solid, sphere, and cylinder<\/li>\n<\/ul>\n<\/section>\n<h2>Journey into 3D Geometry: Exploring Shapes, Volume, and Surface Area<\/h2>\n<p>Welcome to the fascinating world of 3D geometry! Here, we&#8217;ll explore various three-dimensional shapes such as rectangular solids, spheres, cylinders, and cones. We&#8217;ll also delve into how to calculate their volume and surface area. These skills are crucial in fields like engineering, architecture, and physics.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_7081\" aria-describedby=\"caption-attachment-7081\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-7081\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-300x231.jpg\" alt=\"3D shapes including cubes, trapezoids, spheres, and rectangles.\" width=\"500\" height=\"386\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-300x231.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-1024x790.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-768x592.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-1200x925.jpg 1200w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-65x50.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-225x173.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1-350x270.jpg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/18191840\/pexels-crazy-motions-12198530-1.jpg 1520w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-7081\" class=\"wp-caption-text\">Figure 1. Knowing the volumes and surface areas for 3D shapes can be useful for the following tasks<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>You&#8217;re designing a rectangular box for packaging.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9698\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9698&theme=lumen&iframe_resize_id=ohm9698&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Now, let&#8217;s look at how to calculate the surface area of the rectangular solid.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9699\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9699&theme=lumen&iframe_resize_id=ohm9699&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Next, we&#8217;ll move onto spherical shapes which are common in astronomy and physics.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9700\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9700&theme=lumen&iframe_resize_id=ohm9700&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Let&#8217;s consider the surface area of this sphere now.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9701\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9701&theme=lumen&iframe_resize_id=ohm9701&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":23,"menu_order":30,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"3D Render of Shapes\",\"author\":\"crazy motions\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/3d-render-of-shapes-12198530\/\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":71,"module-header":"apply_it","content_attributions":[{"type":"copyrighted_video","description":"3D Render of Shapes","author":"crazy motions","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/3d-render-of-shapes-12198530\/","project":"","license":"arr","license_terms":""}],"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\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4504"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/23"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4504\/revisions"}],"predecessor-version":[{"id":15665,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4504\/revisions\/15665"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/71"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4504\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4504"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4504"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4504"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}