[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297541-105":59,"doc-detail-297541-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","surface-area-of-cylinders-lesson-102-lateral-and-total-surface-area","Surface Area of Cylinders - Lesson 10.2 - Lateral and Total Surface Area","","Lesson focuses on finding the surface area of a cylinder by modeling its curved lateral surface and its two circular bases. It connects formulas for circumference, lateral area, and total surface area, explaining how nets can unfold into a rectangle to match dimensions. Worked examples compute lateral and total areas using given radii, heights, and π = 3.14, then practice problems require rounding to the nearest tenth or whole number. Real-world applications include labels and metal coverings for cans.",{"@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/surface-area-of-cylinders-lesson-102-lateral-and-total-surface-area/297541/",{"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/surface-area-of-cylinders-lesson-102-lateral-and-total-surface-area/297541.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the lateral area of a cylinder?","Question",{"text":113,"@type":114},"Compute the circumference of the base times the cylinder’s height: L = Ch or L = 2πrh.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you find the total surface area of a cylinder?",{"text":118,"@type":114},"Add the areas of the two bases and the lateral area: S = 2B + L or S = 2πr² + 2πrh.",{"name":120,"@type":111,"acceptedAnswer":121},"Why is a net helpful for finding cylinder surface area?",{"text":122,"@type":114},"Unrolling the lateral surface forms a rectangle whose length matches the cylinder’s circumference and whose height matches the cylinder’s height, making the lateral area formula clear.","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},297541,1789745618,{"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":29,"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":130,"read_time":144},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","How do you find the surface area of a cylinder?  \nESSENTIAL QUESTION  \nLESSO N  \nSurface Area of Cylinders  \nExpressions, equations, and relationships—8.7.B  \n… make connections to the formulas for lateral and total surface area and determine solutions for problems involving…cylinders.  \nModeling the Surface Area of a Cylinder  \nJust as you did with a prism, you can use a net to help you find a formula for the surface area of a cylinder.  \nThe lateral area of a cylinder is the area of the curved surface that connects the two bases. The net shows that the lateral surface is a rectangle.  \nUse the diagram of the oatmeal container and its net.  \nImagine unrolling the container’s lateral surface to form a rectangle. What dimension of the cylinder matches the rectangle’s length?  \nWhat dimension of the cylinder matches the rectangle’s height?  \nExpress the lateral area of a cylinder in words and as a formula using the given variables.  \nLateral area = Area of one = Length · Height  \nL = (C = circumference, h = height)  \nL = (r = radius, h = height)  \nExpress the total surface area of a cylinder in words and as a formula using the given variables.  \nTotal surface area = Area of two + Area of one  \nS = (B = base area, C = circumference, h = height) S = (r = radius, h = height)  \nReflect  \n1. Communicate Mathematical Ideas How is the process for finding lateral and total surface area of a cylinder like the process for a prism?  \nr r  \nC = 2πr  \nℓ = 2πr  \nA  \nB  \nThe formula for the circumference of acircle is C = 2πr.  \nC  \nLesson 10.2 275  \n© Houghton Mifflin Harcourt Publ ishing Company  \nMy Notes  \n4 ft  \n7 ft  \n6 cm  \n2.  L:  \n7 ft  \nFinding the Surface Area of a Cylinder  \nThe total surface area of a cylinder is the area of the bases plus the lateral area.  \nFind the lateral and total surface area of the cylinder to the nearest tenth. Use 3.14 for π.  \nFind the lateral area.  \nL = 2πrh ≈ 2(3.14)(4)(7)  \n≈ 175.84  \nThe lateral area is about 175.8 square feet.  \nsurface area.  \nFind the total S = 2πr2 + L  \n≈ 2(3.14)(42) +  \n≈ 100.48 +  \n≈ 276.32 The total surface  \n175.84  \n175.84  \narea of the cylinder is about 276.3 square feet.  \nFind the lateral and total surface area of each cylinder. Round your answers to the nearest tenth. Use 3.14 for π.  \n3. L:  \nUse the formula for the lateral area of a cylinder. Substitute.  \nSimplify.  \nUse the formula for the total surface area of a cylinder.  \nSubstitute.  \nSimplify.  \nAdd.  \nEXAMPLE 1  \n 8.7.B  \nSTEP 1  \nSTEP 2  \nLateral and Total Surface Area of a Cylinder  \nThe lateral area L of a cylinder with height h and radius r is the circumference of the base times the height.  \nL = Ch or L = 2πrh  \nThe total surface area S of a cylinder with height h and radius r is twice the area of a base B plus the lateral area L.  \nS = 2B + L or S = 2πr2 + 2πrh  \nRadius  \nBase  \nHeight  \n© Houghton Mifflin Harcourt Publishing Company  \n276 Unit 3  \n© Houghton Mifflin Harcourt Publishing Company  \nFinding the Surface Area of a Cylinder in a Real-World Situation  \nYou can find many examples of cylinders in your kitchen.  \nThe can shown is 11 inches high and has a diameter of 9 inches. How many square inches of paper are needed for the label? How many square inches of metal are needed to make the entire can? Round your answers to the nearest whole number. Use 3.14 for π.  \nFind the radius of the base.  \nd = 9 in., so r = 4.5 in.  \nTo find the area of the label, find the lateral area.  \nL = 2πrh ≈ 2(3.14)(4.5)(11)  \n≈ 310.86  \nIt takes about 311 square inches of paper to make the label.  \nTo find the amount of metal, find the total surface area. S = 2πr2 + 2πrh  \n≈ 2(3.14)(4.52) + 2(3.14)(4.5)(11)  \n≈ 127.17 + 310.86  \n≈ 438.03  \nIt takes about 438 square inches of metal to make the can.  \nEXAMPLE 2  ~~ ~~ 8.7. B  \nThe radius is half of the diameter.  \nUse the formula for the lateral area of a cylinder.  \nSubstitute.  \nMultiply.  \nUse the formula for the total surface area of a cylinder. Substitute.  \nSimpl","cbCairfhoUWQTGsf","https://ap.wps.com/l/cbCairfhoUWQTGsf","pdf",1549547,"English","# Lesson 10.2: Surface Area of Cylinders\n## Modeling the Surface Area\n## Lateral and Total Surface Area Formulas\n## Finding Surface Area in Real-World Situations\n## Guided Practice\n## Independent Practice","[{\"question\":\"How do you find the lateral area of a cylinder?\",\"answer\":\"Compute the circumference of the base times the cylinder’s height: L = Ch or L = 2πrh.\"},{\"question\":\"How do you find the total surface area of a cylinder?\",\"answer\":\"Add the areas of the two bases and the lateral area: S = 2B + L or S = 2πr² + 2πrh.\"},{\"question\":\"Why is a net helpful for finding cylinder surface area?\",\"answer\":\"Unrolling the lateral surface forms a rectangle whose length matches the cylinder’s circumference and whose height matches the cylinder’s height, making the lateral area formula clear.\"}]","Surface Area of Cylinders - Lesson 10.2 - Lateral and Total Surface Area | PDF",15]