{"id":5396,"date":"2021-03-17T23:41:45","date_gmt":"2021-03-17T23:41:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/summary-solving-problems-using-volume-and-surface-area\/"},"modified":"2021-04-20T03:19:13","modified_gmt":"2021-04-20T03:19:13","slug":"summary-solving-problems-using-volume-and-surface-area","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/summary-solving-problems-using-volume-and-surface-area\/","title":{"raw":"Summary: Solving Problems Using Volume and Surface Area","rendered":"Summary: Solving Problems Using Volume and Surface Area"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul id=\"eip-100\">\r\n \t<li><strong>Volume and Surface Area of a Rectangular Solid<\/strong>\r\n<ul id=\"eip-id3755293\">\r\n \t<li>[latex]V=LWH[\/latex]<\/li>\r\n \t<li>[latex]S=2LH+2LW+2WH[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Volume and Surface Area of a Cube<\/strong>\r\n<ul id=\"eip-id1171779023695\">\r\n \t<li>[latex]V={s}^{3}[\/latex]<\/li>\r\n \t<li>[latex]S=6{s}^{2}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Volume and Surface Area of a Sphere<\/strong>\r\n<ul id=\"eip-id1171783978818\">\r\n \t<li>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]<\/li>\r\n \t<li>[latex]S=4\\pi {r}^{2}[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Volume and Surface Area of a Cylinder<\/strong>\r\n<ul id=\"eip-id1171793481149\">\r\n \t<li>[latex]V=\\pi {r}^{2}h[\/latex]<\/li>\r\n \t<li>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Volume of a Cone<\/strong>\r\n<ul id=\"eip-id1171782886821\">\r\n \t<li>For a cone with radius [latex]r[\/latex] and height [latex]h[\/latex] :Volume: [latex]V=\\Large\\frac{1}{3}\\normalsize\\pi {r}^{2}h[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<dl id=\"fs-id2063975\" class=\"definition\">\r\n \t<dt>cone<\/dt>\r\n \t<dd id=\"fs-id1171505120588\">A cone is a solid figure with one circular base and a vertex.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2036687\" class=\"definition\">\r\n \t<dt>cube<\/dt>\r\n \t<dd id=\"fs-id1417511\">A cube is a rectangular solid whose length, width, and height are equal.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1417515\" class=\"definition\">\r\n \t<dt>cylinder<\/dt>\r\n \t<dd id=\"fs-id1171487155088\">A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.<\/dd>\r\n<\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"eip-100\">\n<li><strong>Volume and Surface Area of a Rectangular Solid<\/strong>\n<ul id=\"eip-id3755293\">\n<li>[latex]V=LWH[\/latex]<\/li>\n<li>[latex]S=2LH+2LW+2WH[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Cube<\/strong>\n<ul id=\"eip-id1171779023695\">\n<li>[latex]V={s}^{3}[\/latex]<\/li>\n<li>[latex]S=6{s}^{2}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Sphere<\/strong>\n<ul id=\"eip-id1171783978818\">\n<li>[latex]V=\\Large\\frac{4}{3}\\normalsize\\pi {r}^{3}[\/latex]<\/li>\n<li>[latex]S=4\\pi {r}^{2}[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Cylinder<\/strong>\n<ul id=\"eip-id1171793481149\">\n<li>[latex]V=\\pi {r}^{2}h[\/latex]<\/li>\n<li>[latex]S=2\\pi {r}^{2}+2\\pi rh[\/latex]<\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume of a Cone<\/strong>\n<ul id=\"eip-id1171782886821\">\n<li>For a cone with radius [latex]r[\/latex] and height [latex]h[\/latex] :Volume: [latex]V=\\Large\\frac{1}{3}\\normalsize\\pi {r}^{2}h[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id2063975\" class=\"definition\">\n<dt>cone<\/dt>\n<dd id=\"fs-id1171505120588\">A cone is a solid figure with one circular base and a vertex.<\/dd>\n<\/dl>\n<dl id=\"fs-id2036687\" class=\"definition\">\n<dt>cube<\/dt>\n<dd id=\"fs-id1417511\">A cube is a rectangular solid whose length, width, and height are equal.<\/dd>\n<\/dl>\n<dl id=\"fs-id1417515\" class=\"definition\">\n<dt>cylinder<\/dt>\n<dd id=\"fs-id1171487155088\">A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-5396\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":12,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"017e26661a4c4f898c1be7d23f415fbe","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5396","chapter","type-chapter","status-publish","hentry"],"part":5375,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/5396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/5396\/revisions"}],"predecessor-version":[{"id":5691,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/5396\/revisions\/5691"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/5375"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/5396\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=5396"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=5396"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=5396"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=5396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}