{"id":10783,"date":"2017-06-05T16:18:37","date_gmt":"2017-06-05T16:18:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10783"},"modified":"2020-01-09T02:04:29","modified_gmt":"2020-01-09T02:04:29","slug":"summary-solving-problems-using-volume-and-surface-area","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/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":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,\r\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\r\n<h2 data-type=\"title\">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 data-type=\"glossary-title\">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>\r\n&nbsp;\r\n<h2 data-type=\"title\"><\/h2>\r\n<h2 data-type=\"title\">Summary of Geometry Formulas<\/h2>\r\nThe following charts summarize all of the formulas covered in this chapter.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224205\/CNX_BMath_Figure_09_06_050a_img.png\" alt=\"A table is shown that summarizes all of the formulas in the chapter. The first cell is for Supplementary and Complementary Angles, and says that the measure of angle A plus the measure of angle B equals 180 degrees for supplementary angles A and B and the measure of angle C plus the measure of angle D equals 90 degrees for complementary angles C and D. There is an image of two angles A and B that together form a straight line and two angles C and D that together form a right angle. The next cell says Rectangular Solid and shows the formulas Volume equals LWH and Surface Area equals 2LH plus 2LW plus 2WH. An image of a rectangular solid with sides L, W, and H is shown. The next cell says Triangle. An image of a triangle is shown with sides a, b, and c, vertices A, B, and C, and height h. It says, \" height=\"\" data-media-type=\"image\/png\" \/>\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224209\/CNX_BMath_Figure_09_06_050c_img.png\" alt=\"This image shows a row with three columns. The first column says Rectangular solid with the formula below that says volume: V equals LWH. Under this, it says Surface Area: S equals 2LH plus 2LW plus 2WH. An image shows an image of a rectangular solid with the sides labeled L , W and H. The middle column says Rectangle. Under this it says Perimeter P equals 2L plus 2W, then Area A equals LW. An image of a rectangle with sides W and L. The right column says Cube. Under this it says \" data-media-type=\"image\/png\" \/>","rendered":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,<br \/>\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\n<h2 data-type=\"title\">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 data-type=\"glossary-title\">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<p>&nbsp;<\/p>\n<h2 data-type=\"title\"><\/h2>\n<h2 data-type=\"title\">Summary of Geometry Formulas<\/h2>\n<p>The following charts summarize all of the formulas covered in this chapter.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224205\/CNX_BMath_Figure_09_06_050a_img.png\" alt=\"A table is shown that summarizes all of the formulas in the chapter. The first cell is for Supplementary and Complementary Angles, and says that the measure of angle A plus the measure of angle B equals 180 degrees for supplementary angles A and B and the measure of angle C plus the measure of angle D equals 90 degrees for complementary angles C and D. There is an image of two angles A and B that together form a straight line and two angles C and D that together form a right angle. The next cell says Rectangular Solid and shows the formulas Volume equals LWH and Surface Area equals 2LH plus 2LW plus 2WH. An image of a rectangular solid with sides L, W, and H is shown. The next cell says Triangle. An image of a triangle is shown with sides a, b, and c, vertices A, B, and C, and height h. It says,\" height=\"\" data-media-type=\"image\/png\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224209\/CNX_BMath_Figure_09_06_050c_img.png\" alt=\"This image shows a row with three columns. The first column says Rectangular solid with the formula below that says volume: V equals LWH. Under this, it says Surface Area: S equals 2LH plus 2LW plus 2WH. An image shows an image of a rectangular solid with the sides labeled L , W and H. The middle column says Rectangle. Under this it says Perimeter P equals 2L plus 2W, then Area A equals LW. An image of a rectangle with sides W and L. The right column says Cube. Under this it says\" data-media-type=\"image\/png\" \/><\/p>\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-10783\">\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":17533,"menu_order":22,"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":"6e29be64-008a-45ca-a3f1-eb9ff28a96b2","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10783","chapter","type-chapter","status-publish","hentry"],"part":7831,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10783","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10783\/revisions"}],"predecessor-version":[{"id":16139,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10783\/revisions\/16139"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/7831"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/10783\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=10783"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=10783"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=10783"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=10783"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}