{"id":1293,"date":"2020-07-11T13:24:26","date_gmt":"2020-07-11T05:24:26","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1293"},"modified":"2022-04-07T15:06:14","modified_gmt":"2022-04-07T07:06:14","slug":"areas-and-volumes","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/areas-and-volumes\/","title":{"rendered":"11. \u9762\u7a4d\u548c\u9ad4\u7a4d (Areas and Volumes)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1293\" class=\"elementor elementor-1293\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-266e1ea elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"266e1ea\" 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-1eaa2fe\" data-id=\"1eaa2fe\" 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-dd9c664 elementor-widget elementor-widget-text-editor\" data-id=\"dd9c664\" 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>\u9762\u7a4d\u53ca\u9ad4\u7a4d\u53c8\u4fc2\u4e00\u500b\u5927\u5bb6\u521d\u4e2d\u5e74\u5e74\u90fd\u8981\u5b78\u5605\u8ab2\u984c\u3002\u55ba\u4e2d\u4e00\u5605\u6642\u5019\u5927\u5bb6\u5176\u5be6\u53ea\u7d93\u5b78\u5497\u4e0d\u5c11\uff0c\u4e2d\u4e8c\u52a0\u5605\u61c9\u8a72\u4e3b\u8981\u4fc2\u6247\u5f62\u5605\u9762\u7a4d\u540c\u5f27\u9577\u3002<\/p><h2>11.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5713\u5f62 (Circle)<\/h2><p>\u5047\u8a2d\u5713\u5f62\u7684\u534a\u5f91\u70ba r \uff0c\u5176\u5468\u754c(\u5373\u5713\u5468)\u53ca\u9762\u7a4d\u7684\u516c\u5f0f\u662f<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(\u5713\u5468 (Circumference) = 2\\pi r\\)<\/li><li>\\( \u5713\u9762\u7a4d (Area of a circle) = \\pi r^{2}\\)<\/li><\/ul><\/li><\/ul><p>\u5176\u5be6\u7121\u54a9\u7279\u5225\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-6caefee elementor-widget elementor-widget-text-editor\" data-id=\"6caefee\" 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>11.2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6247\u5f62 (Sector)<\/h2><p><img decoding=\"async\" class=\"size-full wp-image-1446 alignright\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_sector.gif\" alt=\"\u6247\u5f62\" width=\"141\" height=\"134\" \/>\u5047\u8a2d\u5713\u5f62\u7684\u534a\u5f91\u70ba r \uff0c\u7576\u4f62\u4fc2\u4e00\u500b\u86cb\u7cd5\u5481\u5207\u4e00\u4ef6\u51fa\u569f\u3002\u6240\u5f97\u5605\u5c31\u4fc2\u4e00\u500b\u6247\u5f62\u3002\u7559\u610f\u9664\u5497\u534a\u5f91\u4ee5\u5916\uff0c\u6247\u5f62\u55ba\u5713\u5f62\u4f4d\u7f6e\u7684\u89d2\u90fd\u6703\u5f71\u97ff\u5230\u6247\u5605\u5927\u5c0f\u540c\u5f62\u72c0\u3002<\/p><p>\u6247\u5f62\u7684\u5f27\u9577\u540c\u9762\u7a4d\u7684\u516c\u5f0f\u662f<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(\u5f27\u9577 (Arc length) = 2\\pi r \\times \\dfrac{\\theta}{360^{\\circ}}\\)<\/li><li>\\(\u6247\u5f62\u9762\u7a4d (Sector area) = \\pi r^{2} \\times \\dfrac{\\theta}{360^{\\circ}}\\)<\/li><\/ul><\/li><\/ul><p>\u5fc3\u6c34\u6e05\u5605\u540c\u5b78\u61c9\u8a72\u6703\u7559\u610f\u5230\u6247\u5f62\u5605\u516c\u5f0f\u540c\u5713\u5605\u516c\u5f0f\u597d\u4f3c\u3002\u7121\u932f\uff0c\u662f\u4fc2\u4e58\u591a\u5497\u4e00\u500b\\(\\dfrac{\\theta}{360^{\\circ}}\\)\u3002\u9019\u662f\u56e0\u4e00\u500b\u5713\u5f62\u5605\u5713\u5fc3\u4fc2360\u5ea6\uff0c\u6240\u4ee5\u5982\u679c\u6247\u5f62\u5605\u89d2\u4fc2<span class=\"ILfuVd\"><span class=\"e24Kjd\">\u03b8<\/span><\/span>\uff0c\u6240\u4ee5\u53ef\u4ee5\u6309\u6bd4\u4f8b\u4e58\u8fd4\\(\\dfrac{\\theta}{360^{\\circ}}\\)\u5f97\u51fa\u6247\u5f62\u5605\u5f27\u9577\u53ca\u9762\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-0c324eb elementor-widget elementor-widget-text-editor\" data-id=\"0c324eb\" 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>11.3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5713\u67f1\u9ad4 (Cylinder)<\/h2><p><img decoding=\"async\" class=\"size-full wp-image-1448 alignright\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f1maths_area_cylinder.gif\" alt=\"\u5713\u67f1\u9ad4\" width=\"147\" height=\"159\" \/>\u5713\u67f1\u9ad4\u5605\u9762\u7a4d\u53ca\u9ad4\u7a4d\u7684\u76f8\u95dc\u516c\u5f0f\u5982\u4e0b\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\( \u9ad4\u7a4d = \u5e95\u9762\u7a4d (base area ) \\times \u9ad8 = \\pi r^{2}h \\)<\/li><li>\\(\u66f2\u9762\u9762\u7a4d (Curved surface area) = \u5713\u5468 \\times \u9ad8 = 2\\pi rh \\)<\/li><li>\\(\u7e3d\u9762\u7a4d = \u5e95\u5713\u9762\u7a4d + \u9802\u5713\u9762\u7a4d\u00a0 + \u66f2\u9762\u9762\u7a4d = 2\\pi rh + 2\\pi r^{2}h \\)<\/li><\/ul><\/li><\/ul><p>\u00a0<\/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-cb2eb72 elementor-widget elementor-widget-text-editor\" data-id=\"cb2eb72\" 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>\u5982\u89ba\u81ea\u5df1\u6578\u5b78\u57fa\u790e\u5514\u597d\uff0c\u5927\u53ef\u91cd\u6eab\u4e00\u5413\u4e2d\u4e00\u6642\u5b78\u5497\u54a9\u3002\u8acb\u6309\u300c<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/area-and-volume\/\">\u4e2d\u4e00|\u9762\u7a4d\u53ca\u9ad4\u7a4d<\/a>\u300d<\/p>\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-07c7ab1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"07c7ab1\" 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-2a2e03b\" data-id=\"2a2e03b\" 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-f8b54f2 elementor-widget elementor-widget-text-editor\" data-id=\"f8b54f2\" 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\/form2_maths\/trigonometric-ratios\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u4e09\u89d2\u6bd4<\/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-3a2321c\" data-id=\"3a2321c\" 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-bdc896f\" data-id=\"bdc896f\" 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-5162d4b elementor-widget elementor-widget-text-editor\" data-id=\"5162d4b\" 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\/form2_maths\/statistics\/\">\u7d71\u8a08 <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-c96cfa3\" data-id=\"c96cfa3\" 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-4b2fd44 elementor-widget elementor-widget-sidebar\" data-id=\"4b2fd44\" 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-3 > ul > li > a, .custom-menu-widget .ocean_custom_menu-3 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-3.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e8c\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-3 left dropdown-hover\"><ul id=\"menu-form2mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1248\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1248\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/approximation-errors\/\" class=\"menu-link\">1. \u8fd1\u4f3c\u8207\u8aa4\u5dee (Approximation &#038; Errors)<\/a><\/li>\n<li  id=\"menu-item-1261\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1261\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/identities\/\" class=\"menu-link\">2. \u6046\u7b49\u5f0f (Identities)<\/a><\/li>\n<li  id=\"menu-item-1266\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1266\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/factorization\/\" class=\"menu-link\">3. \u56e0\u5f0f\u5206\u89e3 (Factorization)<\/a><\/li>\n<li  id=\"menu-item-1265\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1265\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/formulae\/\" class=\"menu-link\">4. \u516c\u5f0f (Formulae)<\/a><\/li>\n<li  id=\"menu-item-1278\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1278\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/simultaneous-linear-equations\/\" class=\"menu-link\">5. \u806f\u7acb\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b (Simultaneous Linear Equations)<\/a><\/li>\n<li  id=\"menu-item-1279\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1279\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/rate-and-ratio\/\" class=\"menu-link\">6. \u7387\u53ca\u6bd4 (Rate and Ratio)<\/a><\/li>\n<li  id=\"menu-item-1280\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1280\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/use-of-percentage\/\" class=\"menu-link\">7. \u767e\u4efd\u6cd5 (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1302\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1302\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/geometry\/\" class=\"menu-link\">8. \u5e7e\u4f55\u5b9a\u7406 (Geometry)<\/a><\/li>\n<li  id=\"menu-item-1303\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1303\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/pythagoras-theorem\/\" class=\"menu-link\">9. \u7562\u6c0f\u5b9a\u7406 (Pythagoras\u2019 Theorem)<\/a><\/li>\n<li  id=\"menu-item-1304\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1304\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/trigonometric-ratios\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4 (Trigonometric Ratios)<\/a><\/li>\n<li  id=\"menu-item-1305\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1305\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/areas-and-volumes\/\" class=\"menu-link\">11. \u9762\u7a4d\u548c\u9ad4\u7a4d (Areas and Volumes)<\/a><\/li>\n<li  id=\"menu-item-1306\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1306\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/statistics\/\" class=\"menu-link\">12. \u7d71\u8a08 (Statistics)<\/a><\/li>\n<li  id=\"menu-item-16137\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16137\"><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>\u9762\u7a4d\u53ca\u9ad4\u7a4d\u53c8\u4fc2\u4e00\u500b\u5927\u5bb6\u521d\u4e2d\u5e74\u5e74\u90fd\u8981\u5b78\u5605\u8ab2\u984c\u3002\u55ba\u4e2d\u4e00\u5605\u6642\u5019\u5927\u5bb6\u5176\u5be6\u53ea\u7d93\u5b78\u5497\u4e0d\u5c11\uff0c\u4e2d\u4e8c\u52a0\u5605\u61c9\u8a72\u4e3b\u8981\u4fc2\u6247\u5f62\u5605\u9762\u7a4d\u540c\u5f27 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1238,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-1293","page","type-page","status-publish","hentry","entry"],"yoast_head":"<!-- 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