[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297678-105":59,"doc-detail-297678-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","solid-mensuration-cone-total-surface-area-and-volume-of-a-cone","Solid Mensuration - Cone - Total Surface Area and Volume of a Cone","","Lesson plan for teaching solid mensuration focused on cones, covering key geometry definitions and surface/volume computations. Students learn to define a cone, state formulas for volume and total surface area, determine curved surface area, and calculate cone volume using relationships among radius, slant height, and vertical height (L^2=h^2+r^2). Activities progress from prior-idea identification and guided group exploration through discussion of worked examples and individual application, ending with evaluation questions and a frustum of a cone reading assignment.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/solid-mensuration-cone-total-surface-area-and-volume-of-a-cone/297678/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/solid-mensuration-cone-total-surface-area-and-volume-of-a-cone/297678.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What prior ideas do students build on for this lesson on a cone?","Question",{"text":113,"@type":114},"Students start by defining a cone as a solid with a circular base and slant height, based on the teacher-guided identification of prior ideas.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What formulas are used to calculate volume and surface areas of a cone?",{"text":118,"@type":114},"Volume is given by 1/3πr^2h. Curved surface area is CSA=πrl, and total surface area is TSA=πr(r+l), with L^2=h^2+r^2 relating slant height, height, and radius.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the vertical cone example solved?",{"text":122,"@type":114},"Using the given base diameter 16cm gives r=8cm, then CSA is computed as (22×8×17)/7. For volume, h is found from h^2=427.4285^2−8^2, and Vol=1/3×22/7×8^2×13.5 results in 905cm^3.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},297678,1790084062,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","Date: 25/4/25  \nTheme: Solid Mensuration  \nUnit topic: Cone  \nLesson topic: Total Surface Area and Volume of a Cone  \nTime: 11:00-11:30am  \nDuration: 30 minutes  \nPeriod: fifth  \nSpecific Objectives: At the end of the lesson, the students should be able to;  \n1. Define Cone  \n2. State the volume and total surface area of a cone  \n3. Find the curved surface area of a cone  \n4. Calculate the volume of a cone Instructional Resources: football cone Presentation:  \nStep 1 : Identification of student’s prior ideas.  \nMode: Individual  \nTeacher’s Role: The teacher leads the students todefine a cone as a solid shape with circular base and slant height.  \nStudent’s role: The studentsdefined a cone Step 2: Exploration  \nMode: Group  \nTeacher’s role: The teacher guides the students to state the formulars as follows: Volume= 1/3πr^2h  \nCSA = πrl TSA = πr(r+l)  \nWhile, L, h and r are related by:  \nL^2 = h^2 + r^2  \nStudent’s role: the students stated the above formulars Step 3 : Discussion  \nMode: Group  \nTeacher’s role: The teacher aids the students to solve, thus: a vertical cone has a base diameter 16cm and slant height of 17cm. Find the:  \nI. Curved surface area  \nII. Volume of the cone Solution  \nr = 16/2 = 8cm  \nCSA = πrl  \n= (22×8×17)÷7  \n= 427.43cm  \nStudents’ role: the students asked questions where necessary Step 4: Application  \nMode: Individual  \nTeacher’s role: The teacher asks the studens to find the volume of the above question Students’ role: solution  \nVol = 1/3πr^2h  \nWhere h^2 = 427.4285^2-8^2  \nh =√ 182.6311226  \nh = 13.5 cm Vol = ⅓ × 22/7 × 8^2 × 13.5 = 19008÷21  \n= 905cm^3 Step 5 : Evaluation  \nThe teacher asks the students to:  \n1. Define Cone  \n2. State the volume and total surface area of a cone  \n3. Find the curved surface area of a cone  \n4. Calculate the volume of a cone  \nAssignment: The teacher asks the students to read on frustrum of a cone  \nReferences: 1. New General Mathematics by M. F Macrae et al. 2. New Concept Mathematics by HN Odogwu et al.  \n3. Hidden Facts in Mathematics by M.A. Otumudia","cbCaih81kgufyUfI","https://ap.wps.com/l/cbCaih81kgufyUfI","pdf",48300,"English","# Solid Mensuration\n## Cone: Total Surface Area and Volume","[{\"question\":\"What prior ideas do students build on for this lesson on a cone?\",\"answer\":\"Students start by defining a cone as a solid with a circular base and slant height, based on the teacher-guided identification of prior ideas.\"},{\"question\":\"What formulas are used to calculate volume and surface areas of a cone?\",\"answer\":\"Volume is given by 1/3πr^2h. Curved surface area is CSA=πrl, and total surface area is TSA=πr(r+l), with L^2=h^2+r^2 relating slant height, height, and radius.\"},{\"question\":\"How is the vertical cone example solved?\",\"answer\":\"Using the given base diameter 16cm gives r=8cm, then CSA is computed as (22×8×17)/7. For volume, h is found from h^2=427.4285^2−8^2, and Vol=1/3×22/7×8^2×13.5 results in 905cm^3.\"}]","Solid Mensuration - Cone - Total Surface Area and Volume of a Cone | PDF",1789746884]