[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297451-105":59,"doc-detail-297451-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-and-volumes-introduction-curved-surface-area","Surface Area and Volumes Introduction - Curved Surface Area","","Surface Area and Volumes Introduction explains how everyday solids can be formed by combining basic shapes and how to compute their visible surface areas. It derives total surface area for composite solids using curved surface areas of component shapes while excluding hidden base areas. The guide provides important formulas for common solids such as cuboid, right circular cylinder, sphere, hemisphere, and right circular cone, then applies them through worked examples involving circus tents and cylindrical solids with conical cavities or scooped hemispheres.",{"@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-and-volumes-introduction-curved-surface-area/297451/",{"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-and-volumes-introduction-curved-surface-area/297451.png","ImageObject",300,407,{"name":92,"@type":93},"Melati","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you calculate the total surface area of a combined solid?","Question",{"text":113,"@type":114},"Add the curved surface areas of the component shapes and exclude the base areas that are attached and not visible. Only the parts visible to the eye are included.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What do TSA and CSA stand for in these formulas?",{"text":118,"@type":114},"TSA means Total Surface Area and CSA means Curved Surface Area.",{"name":120,"@type":111,"acceptedAnswer":121},"What surfaces are used to find the total canvas of a circus tent?",{"text":122,"@type":114},"The total canvas equals the curved surface area of the cylindrical base plus the curved surface area of the conical roof.","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},297451,1790310244,{"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":19,"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":52},962085570644,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Surface Area and Volumes Introduction  \nIn our daily life, we come across many objects which areacombination of two or more of the basic solids.  \nSolids have three dimensions-length, breadth, height or depth. Example: book, football, ice cream cone.  \n• A conical circus tent with a cylindrical base.  \n• An ice cream cone is a combination of a cone and a hemisphere.  \n• A test tube used in Science Laboratory is a combination of cylinder and hemisphere.  \nSurface area of a combination of solids  \nLet us consider an example of a circus tent, the tent consists of a cylindrical base surmounted by a conical roof.  \nThe total surface area of the tent  \n= Curved surface area of the cone + Curved Surface area of the cylinder  \n= 􀫈􀜚􀜔 + 􀫛􀫈􀜚􀜐  \nSuppose we have to make a toy by putting together a hemisphere and a cone.  \nSurface area of the toy = Curved Surface Area of hemisphere + Curved Surface Area of cone  \n= 􀫛􀫈􀜚􀫛 + 􀫈􀜚􀜔  \nWhen we are calculating the surface area of combined figures, we should only calculate the areas which are visible to our eyes. For example, an icecream cone is a combination of a cone and a hemisphere. If we have to find the total surface area of this solid, then we add the curved surface areas of the cone and the hemisphere, leaving their base areas as they are attached together and not visible to our eyes.  \nImportant Formulae  \nTSA = Total surface Area and CSA = Curved Surface Area  \n| Cuboid | TSA = 􀫛 (􀜔􀜊 + 􀜊􀜐 + 􀜔􀜐) Volume = 􀜔 × 􀜊 × 􀜐 |\n| --- | --- |\n| Right Circular Cylinder | CSA= 􀫛􀫈􀜚􀜐\u003Cbr>TSA = CSA + Area of two circular ends TSA = 􀫛􀫈􀜚􀜐 + 􀫛􀫈􀜚􀫛\u003Cbr>Volume =􀫈􀜚􀫛 􀜐\u003Cbr>|\n| Sphere | Surface Area of Sphere = 􀫝􀫈􀜚􀫛\u003Cbr>\u003Cbr>Volume of sphere = 􀫝􀫜 􀫈􀜚􀫜\u003Cbr>\u003Cbr>|\n| Hemisphere | Surface Area of Hemisphere = 􀫛􀫈􀜚􀫛 TSA = CSA + Area of circular end\u003Cbr>= 􀫛􀫈􀜚􀫛 + 􀫈􀜚􀫛 = 􀫜􀫈􀜚􀫛\u003Cbr>Volume = 􀫛􀫜 􀫈􀜚􀫜 |\n\n\n| Right Circular Cone | Slant height, 􀜔 = √􀜚􀫛 + 􀜐 􀫛 CSA = 􀫈􀜚􀜔\u003Cbr>TSA = CSA + Area of circular end = 􀫈􀜚􀜔 + 􀫈􀜚􀫛 = 􀫈􀜚 (􀜔 + 􀜚) |\n| --- | --- |\n\nVolume = 􀫚􀫜 􀫈􀜚􀫛 􀜐  \nExample: A circus tent is cylindrical upto a height of 3 m and conical above it. If the diameter of the base is 140 m and the slant height of the conical part is 53 m, find the total canvas used in making the tent.  \nTotal canvas used = Curved Surface Area of cylinder + Curved Surface area of the cone.  \nSlant height of the conical part = 53 m Curved Surface Area of cylinder = 􀫛􀫈􀜚􀜐 Curved Surface Area of cone = 􀫈􀜚􀜔 Total canvas used =􀫛􀫈􀜚􀜐 + 􀫈􀜚􀜔= 􀫈􀜚(􀫛􀜐 + 􀜔) = 􀫛􀫛􀫠 × 􀫚~~ ~~􀫝􀫛􀫙 × (􀫛 × 􀫜 + 􀫞􀫜)  \n= 􀫛􀫛􀫠 × 􀫚~~ ~~􀫝􀫛􀫙 × (􀫛 × 􀫜 + 􀫞􀫜) = 􀫛􀫛􀫠 × 􀫠􀫙 × 􀫞􀫢 = 􀫛􀫛 × 􀫚􀫙 × 􀫞􀫢= 􀫚􀫛􀫢􀫡􀫙 􀜋􀜕 􀫛  \nExample: From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest 􀜋􀜕 􀫛 .  \n(REFERENCE: NCERT)  \nTotal surface area of the remaining solid =  \nCurved Surface Area of the cylinder + Area of the base of the cylinder + Curved Surface Area of the cone Now, Curved Surface Area of cylinder = 􀫛􀫈􀜚􀜐 Curved Surface Area of base of the cylinder = 􀫈􀜚􀫛 Curved Surface Area of cone = 􀫈􀜚􀜔  \nSlant height of the cone, 􀜔 = √􀜚􀫛 + 􀜐 􀫛  \n􀜔 = √(􀫙 . 􀫠)􀫛 + (􀫛 . 􀫝)􀫛 = 􀫛 . 􀫞 􀜋􀜕  \nTotal surface area of the remaining solid =􀫛􀫈􀜚􀜐 + 􀫈􀜚􀫛 + 􀫈􀜚􀜔  \n= 􀫛􀫛 × 􀫚 .􀫝 × 􀫛 × 􀫛 􀫝 + 􀫛􀫛 × ( 􀫚 .􀫝)􀫛 + 􀫛􀫛 × 􀫚 .􀫝 × 􀫛 􀫞  \n􀫠 􀫛 . 􀫠 􀫛 􀫠 􀫛 .  \n= 􀫚􀫚 × 􀫙 . 􀫝 × 􀫛 . 􀫝 + 􀫛􀫛 × 􀫙 . 􀫚 × 􀫙 . 􀫠 + 􀫛􀫛 × 􀫙 . 􀫚 × 􀫛 . 􀫞= 􀫚􀫙 . 􀫞􀫟 + 􀫚 . 􀫞􀫝 + 􀫞 . 􀫞 = 􀫚􀫠 . 􀫟 􀜋􀜕 􀫛  \nExample: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.  \n(REFERENCE: NCERT)  \nTotal Surface Area of the article  \n= Curved Surface Area of the cylinder + 􀫛 × Curved Surface Area of the hemisphere  \nNow, Curved Surface Area of cylinder = 􀫛􀫈􀜚􀜐 Curved Surface Area of hemisphere = 􀫛􀫈􀜚􀫛 Total Surface Area of the article =  \n􀫛􀫈􀜚􀜐 + 􀫛 × 􀫛􀫈􀜚􀫛 = 􀫛􀫈􀜚 (􀜐 + 􀫛􀜚)= 􀫛 × 􀫛􀫛􀫠 × 􀫜 . 􀫞 × (􀫚􀫙 + 􀫛 × 􀫜 . 􀫞) = 􀫝􀫝 × 􀫙 . 􀫞 × 􀫚􀫠 = 􀫜􀫠􀫝 􀜋􀜕 􀫛","cbCaiqyw5efPdiGq","https://ap.wps.com/l/cbCaiqyw5efPdiGq","pdf",240911,"English","# Surface Area and Volumes Introduction\n## Basic solids and examples of combinations\n## Surface area of combinations of solids\n## Important formulae for common solids\n## Worked examples for total surface area","[{\"question\":\"How do you calculate the total surface area of a combined solid?\",\"answer\":\"Add the curved surface areas of the component shapes and exclude the base areas that are attached and not visible. Only the parts visible to the eye are included.\"},{\"question\":\"What do TSA and CSA stand for in these formulas?\",\"answer\":\"TSA means Total Surface Area and CSA means Curved Surface Area.\"},{\"question\":\"What surfaces are used to find the total canvas of a circus tent?\",\"answer\":\"The total canvas equals the curved surface area of the cylindrical base plus the curved surface area of the conical roof.\"}]","Surface Area and Volumes Introduction - Curved Surface Area | PDF",1789744705]