{"id":1505,"date":"2020-07-20T23:36:44","date_gmt":"2020-07-20T15:36:44","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1505"},"modified":"2020-11-02T23:41:44","modified_gmt":"2020-11-02T15:41:44","slug":"area-volume","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/","title":{"rendered":"7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1505\" class=\"elementor elementor-1505\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8a6a373 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8a6a373\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-3b57f04\" data-id=\"3b57f04\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5151b3d elementor-widget elementor-widget-text-editor\" data-id=\"5151b3d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>7.1\u00a0 \u9762\u7a4d\u53ca\u9ad4\u7a4d &#8211; \u57fa\u790e\u77e5\u8b58<\/h2><p>\u300c\u9762\u7a4d\u53ca\u9ad4\u7a4d\u300d\u53c8\u4fc2\u4e00\u500b\u521d\u4e2d\u5e74\u5e74\u90fd\u898b\u5427\u8ab2\u984c\u3002\u6bcf\u5e74\u5b78\u5605\u5622\u5176\u5be6\u5514\u591a\uff0c\u53ea\u4fc2<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\u8981\u6c42\u5927\u5bb6\u4ef2\u8a18\u5f97\u4ee5\u524d\u5b78\u904e\u5605\u516c\u5f0f<\/li><li>\u984c\u76ee\u6703\u4e00\u5e74\u6bd4\u4e00\u5e74\u9577 (\u9577\u53c8\u672a\u5fc5\u4fc2\u6df1)<\/li><\/ul><\/li><\/ul><p>\u5728\u6b64\uff0c\u5927\u5bb6\u6700\u597d\u5148\u6eab\u7fd2\u4e00\u5413<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/area-and-volume\/\">\u4e2d\u4e00<\/a>\u3001<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/areas-and-volumes\/\">\u4e2d\u4e8c<\/a>\u5b78\u904e\u5605\u9762\u7a4d\u53ca\u9ad4\u7a4d\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eca93b6 elementor-widget elementor-widget-text-editor\" data-id=\"eca93b6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>7.2\u00a0 \u68f1\u9310 (Pyramid)<\/h2><p><img decoding=\"async\" class=\"size-full wp-image-1583 alignright\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_pyramid.jpg\" alt=\"\u68f1\u9310\" width=\"188\" height=\"248\" \/>\u68f1\u9310\u662f\u4e00\u500b\u5e95\u70ba\u591a\u908a\u5f62\u7684\u5c16\u5854\u3002<\/p><p>\u55ba\u521d\u4e2d\u554f\u5f97\u5927\u5bb6\u5605\uff0c99%\u90fd\u4fc2\u6b63\u68f1\u9310\uff0c\u5373\u5e95\u5716\u5f62\u4fc2\u4e00\u500b\u6b63\u591a\u908a\u5f62\uff0c\u800c\u500b\u5c16\u9802\u4fc2\u55ba\u6b63\u500b\u5e95\u5605\u4e2d\u5fc3\u4e0a\u65b9\u3002\u800c\u6bcf\u500b\u5074\u9762\u90fd\u4fc2\u4e00\u6a23\u5605\u3002<\/p><ul><li>\\( \u9ad4\u7a4d = \\dfrac{1}{3}\\times \u5e95\u9762\u7a4d \\times \u9ad8\\)<\/li><li>\u7e3d\u8868\u9762\u9762\u7a4d = \u6240\u6709\u5074\u9762\u7684\u7e3d\u9762\u7a4d + \u5e95\u9762\u7a4d<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-beadedb elementor-widget elementor-widget-text-editor\" data-id=\"beadedb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>7.3\u00a0 \u5713\u9310 (Cone)<\/h2><p><img decoding=\"async\" class=\"alignright wp-image-1582 size-thumbnail\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_cone-150x150.png\" alt=\"\u5713\u9310\u5f62\" width=\"150\" height=\"150\" \/>\u5713\u9310\u662f\u4e00\u500b\u5e95\u70ba\u5713\u5f62\u7684\u5c16\u5854\u3002<\/p><p>\u9664\u4e86\u9ad8\u5ea6\u5916\uff0c\u6211\u5011\u9084\u8981\u7559\u610f\u5713\u9310\u6709\u4e00\u500b\u201c\u659c\u9ad8\u201d\u3002\u201c\u659c\u9ad8\u201d\u662f\u5e95\u90e8\u5713\u5468\u4e0a\u7684\u4e00\u9ede\u8207\u9802\u9ede\u7684\u9023\u7dda\u7684\u9577\u5ea6\u3002<\/p><ul><li>\u7559\u610f r\u3001h\u3001l \u4fc2\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e09\u908a\u3002\u800c\u6309\u7562\u6c0f\u5b9a\u7406:<br \/>\\(\\quad r^{2} + h^{2} = l^{2}\\)<\/li><li>\\( \u9ad4\u7a4d = \\dfrac{1}{3}\\times \u5e95\u9762\u7a4d \\times \u9ad8 = \\dfrac{1}{3}\\pi r^{2}h\\)<\/li><li>\\(\u66f2\u9762\u9762\u7a4d\u00a0 = \\pi \\times r \\times l \\)<\/li><li>\\(\u7e3d\u8868\u9762\u9762\u7a4d \uff1d \u66f2\u9762\u9762\u7a4d + \u5e95\u9762\u7a4d \uff1d \\pi r l + p r^{2}\\)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d55434 elementor-widget elementor-widget-text-editor\" data-id=\"4d55434\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>7.4\u00a0 \u7403\u9ad4<\/h2><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignright wp-image-1584 size-medium\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_sphere-300x284.png\" alt=\"\u7403\u9ad4\" width=\"300\" height=\"284\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_sphere-300x284.png 300w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_sphere.png 580w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\u7403\u9ad4\u5373\u4fc2\u4e00\u500b\u6ce2\u3002<\/p><ul><li>\\(\u9ad4\u7a4d = \\dfrac{4}{3}\\pi r^{3}\\)<\/li><li>\\(\u8868\u9762\u9762\u7a4d = 4\\pi r^{2}\\)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ffc355 elementor-widget elementor-widget-text-editor\" data-id=\"2ffc355\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>7.5\u00a0 \u76f8\u4f3c\u5f62\u72c0<\/h2><p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1585 alignright\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_similarFig.jpg\" alt=\"\u76f8\u4f3c\u5f62\u72c0\" width=\"257\" height=\"196\" \/>\u8981\u7406\u89e3\u54a9\u4fc2\u76f8\u4f3c\u5f62\u72c0\uff0c\u5927\u5bb6\u53ea\u8981\u8ad7\u5413\u53ee\u5679(\u591a\u5566A\u5922)\u5605\u8b8a\u5927\u7e2e\u5c0f\u69cd\u5c31\u53ef\u4ee5\u4e86\u3002<\/p><p>\u5c0d\u65bc\u5169\u500b\u76f8\u4f3c\u5f62\u72c0\uff0c\u5982\u679cl<sub>1<\/sub> \u548c l<sub>2<\/sub> \u662f\u4efb\u4f55\u5169\u689d\u5c0d\u61c9\u908a\u7684\u9577\u5ea6\uff0c\u5247\u5b83\u5011\u7684\u8868\u9762\u9762\u7a4d\u6bd4\uff08A<sub>1<\/sub> : A<sub>2<\/sub>\uff09\u548c\u9ad4\u7a4d\u6bd4( V<sub>1<\/sub>\uff1aV<sub>2<\/sub>)\u662f\uff1a<\/p><ul><li>\\(\\dfrac{A_{1}}{A_{2}} = \\left ( \\dfrac{A_{1}}{A_{2}} \\right )^{2} \\)<\/li><li>\\(\\dfrac{V_{1}}{V_{2}} = \\left ( \\dfrac{A_{1}}{A_{2}} \\right )^{3} \\)<\/li><\/ul><p>\u5927\u5bb6\u7559\u610f\u6709\u6642\u984c\u76ee\u4fc2\u6bd4\u5497\u500b\u9762\u7a4d\u6bd4\u4f60\uff0c\u4f46\u5c31\u8981\u6c42\u4f60\u53bb\u8a08\u9ad4\u7a4d\u6bd4\u3002\u89e3\u984c\u5605\u6280\u5de7\u4fc2<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\u5148\u5229\u7528\u9762\u7a4d\u6bd4\u8a08\u51fa\u500b\u908a\u9577\u6bd4<\/li><li>\u518d\u5229\u7528\u908a\u9577\u6bd4\u8a08\u9ad4\u7a4d\u6bd4<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-df67b5f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"df67b5f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-b7cf196\" data-id=\"b7cf196\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cbe772e elementor-widget elementor-widget-text-editor\" data-id=\"cbe772e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u56db\u908a\u5f62<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-c691808\" data-id=\"c691808\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-67a6de2\" data-id=\"67a6de2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b30f38 elementor-widget elementor-widget-text-editor\" data-id=\"5b30f38\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\">\u5750\u6a19\u5e7e\u4f55 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f24cfc1\" data-id=\"f24cfc1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0efa66e elementor-widget elementor-widget-sidebar\" data-id=\"0efa66e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-4 > ul > li > a, .custom-menu-widget .ocean_custom_menu-4 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-4.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e09\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-4 left dropdown-hover\"><ul id=\"menu-form3mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1543\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1543\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/\" class=\"menu-link\">1. \u4e0d\u7b49\u5f0f (Inequalities)<\/a><\/li>\n<li  id=\"menu-item-1542\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1542\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/indices\/\" class=\"menu-link\">2. \u6307\u6578 (Indices)<\/a><\/li>\n<li  id=\"menu-item-1541\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1541\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\" class=\"menu-link\">3. \u767e\u4efd\u6cd5  (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1540\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1540\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/\" class=\"menu-link\">4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)<\/a><\/li>\n<li  id=\"menu-item-1539\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1539\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\" class=\"menu-link\">5. \u6f14\u7e79\u5e7e\u4f55 (Deductive Geometry)<\/a><\/li>\n<li  id=\"menu-item-1538\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1538\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\" class=\"menu-link\">6. \u56db\u908a\u5f62 (Quadrilateral)<\/a><\/li>\n<li  id=\"menu-item-1537\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1537\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\" class=\"menu-link\">7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)<\/a><\/li>\n<li  id=\"menu-item-1536\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1536\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\" class=\"menu-link\">8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)<\/a><\/li>\n<li  id=\"menu-item-1535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1535\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\" class=\"menu-link\">9. \u4e09\u89d2\u5b78 (Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1534\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1534\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4\u7684\u61c9\u7528 (Applications of Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1533\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1533\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" class=\"menu-link\">11. \u6982\u7387 (Probability)<\/a><\/li>\n<li  id=\"menu-item-1532\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1532\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\" class=\"menu-link\">12. \u7d71\u8a08 \u2013 \u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 (Measure of Central Tendency)<\/a><\/li>\n<li  id=\"menu-item-1625\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1625\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/centers-of-triangles\/\" class=\"menu-link\">13. \u4e09\u89d2\u5f62\u7684\u5fc3 (Centers of Triangles)<\/a><\/li>\n<li  id=\"menu-item-16136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>7.1\u00a0 \u9762\u7a4d\u53ca\u9ad4\u7a4d &#8211; \u57fa\u790e\u77e5\u8b58 \u300c\u9762\u7a4d\u53ca\u9ad4\u7a4d\u300d\u53c8\u4fc2\u4e00\u500b\u521d\u4e2d\u5e74\u5e74\u90fd\u898b\u5427\u8ab2\u984c\u3002\u6bcf\u5e74\u5b78\u5605\u5622\u5176\u5be6\u5514\u591a\uff0c 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