[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297699-105":59,"doc-detail-297699-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","volume-and-surface-area-of-a-cylinder-starter","Volume and Surface Area of a Cylinder - Starter","","Learning material focused on the volume and surface area of a cylinder, starting with a review problem about water in a pipe and calculating cross-sectional area and water volume for a given length. It then explains the cylinder as a prism with circular cross-section, deriving V = πr²h. Worked examples cover using radius/diameter, melting a cube to a cylinder, and finding total surface area using curved-area plus two circular ends.",{"@graph":69,"@context":122},[70,84,105],{"@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/volume-and-surface-area-of-a-cylinder-starter/297699/",{"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/volume-and-surface-area-of-a-cylinder-starter/297699.png","ImageObject",300,407,{"name":92,"@type":93},"วิน","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the volume of water in a pipe when only the water depth is given?","Question",{"text":112,"@type":113},"Find the cross-sectional area of the water segment first, using the geometry of the central angle. Then multiply that area by the pipe length to get the water volume.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the general formula for the volume of a cylinder?",{"text":117,"@type":113},"The volume of a cylinder is V = πr²h, where r is the radius and h is the height.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you calculate the total surface area of a cylinder?",{"text":121,"@type":113},"Add the area of the two circular ends and the curved surface area. This gives SA = 2πr² + 2πrh.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},297699,1789747087,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":39},2336475104736,"https://ap-avatar.wpscdn.com/avatar/22000c4c5e0e5b17e70?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786591360781797222","Volume and Surface Area of a Cylinder  \nStarter  \n1. (Review of last lesson)  \nA pipe of radius 7 cm can have a maximum depth of 2 cm.  \n(a) Find the shaded area (cross-sectional area of water) .  \n(b) What is the volume of water in a length of 30 cm of the pipe?  \nHint: Find the distance from O to the surface of the water.  \nWorking: (a) The perpendicular distance  \nfrom O to the surface of water is 7 − 2 = 5  \n∴ cosθ = 57 θ = cos−1 ~~ ~~57 ≈ 44.42o  \nRadius = 7  \nO  \nθ  \n5  \nRadius = 7  \n2  \nSo the angle at the centre is 2θ = 2 cos−1 ~~ ~~57 ≈ 88.83o  \nArea of segment = Area of sector —Area of triangle = ~~ ~~8836.803 × π × 72 − ~~ ~~12 × 7 × 7 × sin88.83 = 13.5 cm2 (3 s.f.)  \n(b) Volume of water = 13.489... × 30 = 404.7 cm3 (4 s.f.)  \nNotes  \nVolume of a cylinder  \nA cylinder is a prism with a circular cross-section. The volume of a prism is given by:  \nVolume of prism = Area of cross-section × Length  \nE.g. 1 Using the formula for the prism, write down the formula for the volume of a cylinder whose radius is r and whose height is h.  \nWorking: Area of cross-section = π r2  \nSo V = π r2 h  \nVolume of a cylinder, V = π r2 h  \nE.g. 2 Calculate the volume of a cylinder whose height is 10 cm and whose diameter is 12 cm Give your answer in terms of π.  \nWorking: Since the diameter is 12 cm, the radius is 6 cm.  \nVolume of a cylinder, V = π × 62 × 10 = 360π cm3  \n.  \nh  \n[www.mathspanda.com](www.mathspanda.com)  \nE.g. 3 A gold cube of side 5 cm is melted down to form a cylinder whose height is 3 cm. Find the cylinder’s radius.  \nWorking: Volume of cube = 53 = 125  \n∴ π × r 2 × 3 = 125  \n125  \n2  \nr = ~~ ~~  \n3π  \nr = ~~ ~~1253π = 3.64 cm  \nSurface area of a cylinder  \nWhat shapes is the surface area of a cylinder made up of?  \n2 circles and a rectangle  \nE.g. 4 Using the diagram below, find a formula for the surface area of a cylinder.  \nWorking:  \n=  \n+  \nThe length of the rectangle is equal to the circumference of the circle.  \nSurface area = Area of circle + Area of circle + Area of rectangle = π r2 + π r2 + 2π r × h = 2π r2 + 2π rh  \nSurface area of cylinder, SA = 2π r2 + 2π rh  \nE.g. 5 Find the total surface area of a cylinder whose radius is 3 cm and whose height is 8 cm. Give your answer in terms of π.  \nWorking: Surface area = 2π r2 + 2π rh  \n= 2π × 32 + 2π × 3 × 8 = 18π + 48π  \n= 66π cm2 (4 s.f.)  \nE.g. 6 A cylinder has total surface area of 110π. Find its height given that its radius is 5 cm.  \nWorking: 2π × 52 + 2π × 5 × h = 110π  \n50π + 10πh = 110π  \n10πh = 60π h = ~~ ~~6010ππ = 6 cm  \n[www.mathspanda.com](www.mathspanda.com)  \nE.g. 7 A label is to cover the curved surface of a baked beans tin. The tin has a diameter of 74 mm and a height of 115 mm. Given that the label will overlap by 1 cm, find the area of the label in:  \n(a) mm2 (b) cm2.  \nWorking: (a) The label is a rectangle whose height is 115 mm  \nThe length of the rectangle is the circumference plus 1 cm Length = 74π + 10 C = πd and 1 cm ≡ 10 mm  \nArea of label = 115(74π + 10) = 27885 mm2 (5 s.f.) and  \n(b) 1 cm ≡ 10 mm so 1 cm2 ≡ 102 mm2 = 100 mm2  \n27885 mm2 ≡ 278.85 cm2 (2 d.p.)  \nVideo:  Volume of a cylinder  \nVideo:  Surface area of a cylinder  \nSolutions to Starter and E.g.s  \nExercise  \n9-1 class textbook: p438 M13 .5 Qu 7-14  \nA*-G class textbook: p393 M13 .2 Qu 7-14  \n9-1 homework book: p150 M13 .5/13 .6 Qu 6-12  \nA*-G homework book: p110 M13 .2 Qu 6-10  \nHomework book answers (only available during a lockdown)","cbCailWOyy4i57MF","https://ap.wps.com/l/cbCailWOyy4i57MF","pdf",207491,"English","# Volume of a cylinder\n## Review: water depth and cross-sectional area\n## Formula derivation: V = πr²h\n# Surface area of a cylinder\n## Components: two circles and a rectangle\n## Total surface area examples","[{\"question\":\"How do you find the volume of water in a pipe when only the water depth is given?\",\"answer\":\"Find the cross-sectional area of the water segment first, using the geometry of the central angle. Then multiply that area by the pipe length to get the water volume.\"},{\"question\":\"What is the general formula for the volume of a cylinder?\",\"answer\":\"The volume of a cylinder is V = πr²h, where r is the radius and h is the height.\"},{\"question\":\"How do you calculate the total surface area of a cylinder?\",\"answer\":\"Add the area of the two circular ends and the curved surface area. This gives SA = 2πr² + 2πrh.\"}]","Volume and Surface Area of a Cylinder - Starter | PDF"]