[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297249-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297249-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","surface-area-of-cylinders-grade-7-math-lesson","Surface Area of Cylinders - Grade 7 Math Lesson","","Surface Area of Cylinders explains how to find the total outside area of a cylinder, combining two circular bases and the curved lateral surface. It presents the key formulas SA = 2πr2 + 2πrh and lateral area LA = 2πrh, with guidance to use radius rather than diameter and to measure square units. Step-by-step examples and a set of practice problems cover total surface area and label/wrapper (lateral-only) situations, using π ≈ 3.14 when requested.",{"@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/surface-area-of-cylinders-grade-7-math-lesson/297249/",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/surface-area-of-cylinders-grade-7-math-lesson/297249.png","ImageObject",300,407,{"name":42,"@type":43},"Finn","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the formula for the total surface area of a cylinder?","Question",{"text":63,"@type":64},"The total surface area is SA = 2πr2 + 2πrh, which includes both circular bases and the curved lateral surface.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find the lateral surface area when a problem asks for “label” or “wrapper” area?",{"text":68,"@type":64},"Use only the curved part: LA = 2πrh, which excludes the top and bottom circles.",{"name":70,"@type":61,"acceptedAnswer":71},"Should you use the radius or the diameter when applying the cylinder surface area formulas?",{"text":72,"@type":64},"Use the radius r. If the problem gives the diameter, convert using r = d/2 before substituting into the formulas.","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},297249,1789743372,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"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":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"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":96,"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":143},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","Surface Area of Cylinders  \n\n| Name:   | D | ate:   | S | core:   / 17 |\n| --- | --- | --- | --- | --- |\n\nThe surface area of a cylinder is the total area of everything on the outside: two circular bases plus the curved surface that wraps around them. Here is a great trick: imagine “unrolling” the curved part into a rectangle—its width equals the circumference of the base (2πr) and its height equals the height of the cylinder. That gives the formula SA = 2πr2 + 2πrh, where the first term covers both bases and the second covers the lateral surface. If you only need the lateral area—like finding how much paper wraps a label—use just LA = 2πrh. As always, double-check that you are using the radius, not the diameter!  \nKey Concepts & Quick Review  \nSurface Area of a Cylinder:  \nSA = 2πr2 + 2πrh  \n2πr2 area of the two circular bases 2πrh lateral (curved) surface area  \nLateral area only (open-top or label-area problems): LA = 2πrh.  \nUse π ≈ 3.14 unless told otherwise. Surface area is measured in square units (cm2 , in 2 , etc.) .  \nExamples  \n➀ Find the total surface area of a cylinder with r = 3 cm and h = 10 cm. Use π ≈ 3.14.  \n¬ Think It Through: A cylinder’s surface area has two parts: the two circular bases and the curved side (lateral area). First, the bases: 2 × 3.14 × 32 = 2 × 3.14 × 9 = 56 .52 cm 2. Next, picture unrolling the curved side into a rectangle whose width is the circumference: 2 × 3.14 × 3 × 10 = 188 .4 cm 2. Add  \nthem up: 56.52 + 188 .4 = 244 .92 cm 2.  \n􀀑 Answer: 244.92 cm 2  \n➁ A can has a diameter of 8 cm and a height of 12 cm. Find the lateral surface area only.¬ Think It Through: The question asks for the lateral area only—that is the curved part, not the top or bottom circles. First find the radius: r = ~~8~~2 = 4 cm. Then apply the lateral-area formula: LA = 2πrh = 2 × 3.14 × 4 × 12 = 301 .44 cm 2. Imagine peeling the label off the can—that is the lateral surface!  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \n􀀑 Answer: 301.44 cm 2  \n✎ Practice Problems  \nFind the total surface area of each cylinder. Use π ≈ 3.14. Round to the nearest hundredth.  \n1. Find the total surface area of a cylinder with radius 4 cm and height 6 cm.  \n2. Find the total surface area of a cylinder with radius 5 in and height 10 in.  \n3. Find the total surface area of a cylinder with diameter 10 m and height 7 m.  \n4. Find the total surface area of a cylinder with radius 2ft and height 9ft.  \n5. Find the total surface area of a cylinder with diameter 14 cm and height 3 cm.  \n6. Find the total surface area of a cylinder with radius 7 in and height 4 in.  \n7. Find the total surface area of a cylinder with radius 1 m and height 15 m.  \n8. Find the total surface area of a cylinder with diameter 8ft and height 5ft.  \nd = 8 ft  \nh = 5 ft  \n9. Find the total surface area of a cylinder with radius 6 cm and height 6 cm.  \n10. Find the total surface area of a cylinder with diameter 12 in and height 8 in.  \nd = 12 in  \nh = 8 in  \n11. Find the total surface area of a cylinder with radius 3 m and height 11 m.  \n12. Find the total surface area of a cylinder with radius 10 cm and height 2 cm.  \n13. Find the total surface area of a cylinder with diameter 6ft and height 14ft.  \nh = 14 ft  \n14. Find the total surface area of a cylinder with radius 8 in and height 1 in.  \n15. Find the total surface area of a cylinder with radius 9 m and height 5 m.  \nr = 9 m  \nh = 5 m  \nStudy Tips  \n☞ Surface area has two parts: the circles on top and bottom (2πr2 ) plus the curved side (2πrh) . Don’t forget either one!  \n☞ If a problem asks for a “label” or “wrapper” area, that is the","cbCairLAL748SqLd","https://ap.wps.com/l/cbCairLAL748SqLd","pdf",329569,"English","# Surface Area Formulas\n## Total surface area (SA)\n## Lateral surface area (LA)\n# Examples\n## Two worked examples\n# Practice Problems\n## Total surface area\n## Lateral-only and word problems\n# Study Tips\n## Common mistakes and unit reminders\n# Word Problems\n## Open-top mug and label wrapper","[{\"question\":\"What is the formula for the total surface area of a cylinder?\",\"answer\":\"The total surface area is SA = 2πr2 + 2πrh, which includes both circular bases and the curved lateral surface.\"},{\"question\":\"How do you find the lateral surface area when a problem asks for “label” or “wrapper” area?\",\"answer\":\"Use only the curved part: LA = 2πrh, which excludes the top and bottom circles.\"},{\"question\":\"Should you use the radius or the diameter when applying the cylinder surface area formulas?\",\"answer\":\"Use the radius r. If the problem gives the diameter, convert using r = d/2 before substituting into the formulas.\"}]","Surface Area of Cylinders - Grade 7 Math Lesson | PDF",13]