[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297383-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297383-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","geometry-part-2-lesson-5-surface-area-and-volume-of-spheres","Geometry - Part 2 - Lesson 5 - Surface Area and Volume of Spheres","","This educational document provides a comprehensive overview of the geometry of spheres, specifically focusing on surface area calculations. It defines key terminology including center, radius, chord, diameter, and great circles. The content explains the mathematical relationship between the radius and surface area, supported by step-by-step examples demonstrating how surface area changes when dimensions are scaled. Additionally, the material covers the properties of intersections between planes and spheres, detailing the formation of great circles and hemispheres. Designed as a study guide, it offers clear formulas and practical application problems to help students master the spatial reasoning and computational requirements for measuring spherical objects in geometry.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/geometry-part-2-lesson-5-surface-area-and-volume-of-spheres/297383/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/geometry-part-2-lesson-5-surface-area-and-volume-of-spheres/297383.png","ImageObject",300,407,{"name":42,"@type":43},"Ava Thompson","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the relationship between the radius and the diameter of a sphere?","Question",{"text":63,"@type":64},"The diameter of a sphere is defined as a chord that passes through the center, and its length is exactly twice the length of the radius.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the formula for calculating the surface area of a sphere?",{"text":68,"@type":64},"The surface area S of a sphere with radius r is calculated using the formula S = 4πr².",{"name":70,"@type":61,"acceptedAnswer":71},"What is a great circle of a sphere?",{"text":72,"@type":64},"A great circle is the intersection of a sphere and a plane that contains the center of the sphere, which effectively divides the sphere into two congruent halves known as hemispheres.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297383,1789744176,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":117,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":103},1649267921044,"https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1786009248482753345","Surface Area and Volume of Spheres  \nFinding the Surface Area of a Sphere  \nA circle is described as a locus of points in a plane that are a given distance from a point. A sphere is the locus of points in space that are a given distance from a point.  \nFinding the Surface Area of a Sphere  \n• The point is called the center of the sphere. A radius of a sphere is a segment from the center to a point on the sphere.  \n• A chord of a sphere is a segment whose endpoints are on the sphere.  \nFinding the Surface Area of a Sphere  \n• A diameter is a chord that contains the center. As with all circles, the terms radius and diameter also represent distances, and the diameter is twice the radius.  \nSurface Area of a Sphere  \n• The surface area of a sphere with radius r is S = 4􀁓r2 .  \nEx. 1: Finding the Surface Area of a Sphere  \n• Find the surface area. When the radius doubles, does the surface area double?  \nS = 4􀁓r2 = 4􀁓22 = 16􀁓 in.2  \nS = 4􀁓r2 = 4􀁓42  \n= 64􀁓 in.2  \nMore . . .  \n• If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a great circle of the sphere. Every great circle of a sphere separates a sphere into two congruent halves called  \nhemispheres.  \nEx. 2: Using a Great Circle  \n• The circumference of a great circle of a sphere is 13.8􀁓 feet. What is the surface area of the sphere?  \nSolution:   \nBegin by finding the radius of the sphere.  \nC = 2􀁓r  \n13.8􀁓 = 2􀁓r  \n13.8􀁓  \n2􀁓r  \n 6.9 = r = r","cbCaioJMa6mIlw09","https://ap.wps.com/l/cbCaioJMa6mIlw09","pdf",767958,"English","# Geometry of Spheres\n## Key Terms and Definitions\n## Surface Area Formula\n## Example Problems and Solutions\n## Great Circles and Hemispheres","[{\"question\":\"What is the relationship between the radius and the diameter of a sphere?\",\"answer\":\"The diameter of a sphere is defined as a chord that passes through the center, and its length is exactly twice the length of the radius.\"},{\"question\":\"What is the formula for calculating the surface area of a sphere?\",\"answer\":\"The surface area S of a sphere with radius r is calculated using the formula S = 4πr².\"},{\"question\":\"What is a great circle of a sphere?\",\"answer\":\"A great circle is the intersection of a sphere and a plane that contains the center of the sphere, which effectively divides the sphere into two congruent halves known as hemispheres.\"}]","Geometry - Part 2 - Lesson 5 - Surface Area and Volume of Spheres | PDF"]