[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297242-105":59,"doc-detail-297242-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","chapter-12-surface-areas-and-volumes-122-surface-area-of-a-combination-of-solids","Chapter 12: Surface Areas and Volumes - 12.2 Surface Area of a Combination of Solids","","Covers 12.2 on total surface area for combinations of solids. Defines TSA as the sum of all outer surfaces and explains that overlapping contact areas between joined solids are excluded. Works through examples including a cylinder with two hemispheres and a cone on a cylinder, giving core formulas and notes about hidden internal bases. Provides an exam-ready step-by-step method, highlights common mistakes, and includes targeted practice scenarios.",{"@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/chapter-12-surface-areas-and-volumes-122-surface-area-of-a-combination-of-solids/297242/",{"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/chapter-12-surface-areas-and-volumes-122-surface-area-of-a-combination-of-solids/297242.png","ImageObject",300,407,{"name":92,"@type":93},"8796093062539","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is TSA (Total Surface Area) for a combination of solids?","Question",{"text":112,"@type":113},"TSA is the sum of all outer surfaces. Areas where solids overlap or are in contact are not counted in the total surface area.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why do overlapping regions not contribute to surface area calculations?",{"text":117,"@type":113},"When two solids are joined, the contact area becomes internal and is not exposed, so it is excluded from TSA.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the main difference between calculating total surface area and total volume?",{"text":121,"@type":113},"For surface area, overlapping contact areas must be subtracted. For volume, overlapping regions do not require subtraction—total volume is obtained by adding individual volumes.","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},297242,1789743346,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":138,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":67,"update_tm":129,"read_time":52},8796093062539,"**Chapter 12: Surface Areas and Volumes **  \n12.2 Surface Area of a Combination of Solids  \nKey Concepts:  \n Total Surface Area (TSA): Sum of all outer surfaces.  \n Overlapping Surfaces: When two solids are joined, the area of contact is not counted in the total surface area.  \nExample 1: Cylinder with Two Hemispheres (Capsule Shape)  \n TSA = Surface area of cylinder + 2 × Surface area of hemisphere (but excluding the base of the hemispheres) .  \n Formula: 2􀟨􀝎ℎ + 2×2􀟨􀝎2 = 2􀟨􀝎(ℎ + 2􀝎)  \n Note: The bases of the hemispheres are internal and not exposed.  \nExample 2: Cone on a Cylinder  \n TSA = Surface area of cylinder (excluding top base) + Surface area of cone (excluding base) .  \n Formula: 2􀟨􀝎ℎ + 􀟨􀝎􀝈 (where 􀝈 = √􀝎 2 + ℎ 2  ) Important Points:  \n Step-by-Step Method:  \n Identify the individual solids in the combination.  \n Calculate their individual surface areas.  \n Subtract the areas of overlapping surfaces.  \n Common Mistake: Forgetting to subtract overlapping areas (e.g. , the base of a hemisphere attached to a cylinder) .  \nExam-Focused Examples:  \n1. A sphere is placed on top of a cube. Calculate the total surface area.  \n2. Solution: Surface area of cube + Surface area of sphere (excluding the base where they are joined) .  \n3. A cone is attached to a hemisphere (like a ice cream cone) .  \n4. TSA = Surface area of hemisphere (excluding base) + Surface area of cone (excluding base) .  \nContact us: [sathee@iitk.ac.in](sathee@iitk.ac.in)  \nVisit us at [https://sathee.iitk.ac.in](https://sathee.iitk.ac.in)  \nPage 1 of 4 © 2023-2025 Copyright SATHEE  \n**Chapter 12: Surface Areas and Volumes **  \n12.2 Surface Area of a Combination of Solids  \nKey Concepts:  \n Total Surface Area (TSA): Sum of all outer surfaces.  \n Overlapping Surfaces: When two solids are joined, the area of contact is not counted in the total surface area.  \nExample 1: Cylinder with Two Hemispheres (Capsule Shape)  \n TSA = Surface area of cylinder + 2 × Surface area of hemisphere (but excluding the base of the hemispheres) .  \n Formula: 2􀟨􀝎ℎ + 2×2􀟨􀝎2 = 2􀟨􀝎(ℎ + 2􀝎)  \n Note: The bases of the hemispheres are internal and not exposed.  \nExample 2: Cone on a Cylinder  \n TSA = Surface area of cylinder (excluding top base) + Surface area of cone (excluding base) .  \n Formula: 2􀟨􀝎ℎ + 􀟨􀝎􀝈 (where 􀝈 = √􀝎 2 + ℎ 2  ) Important Points:  \n Step-by-Step Method:  \n Identify the individual solids in the combination.  \n Calculate their individual surface areas.  \n Subtract the areas of overlapping surfaces.  \n Common Mistake: Forgetting to subtract overlapping areas (e.g. , the base of a hemisphere attached to a cylinder) .  \nExam-Focused Examples:  \n1. A sphere is placed on top of a cube. Calculate the total surface area.  \n2. Solution: Surface area of cube + Surface area of sphere (excluding the base where they are joined) .  \n3. A cone is attached to a hemisphere (like a ice cream cone) .  \n4. TSA = Surface area of hemisphere (excluding base) + Surface area of cone (excluding base) .  \n12.3 Volume of a Combination of Solids  \nKey Concepts:  \n Total Volume: Sum of the volumes of individual solids.  \n No Subtraction: Unlike surface area, overlapping regions do not affect volume.  \nContact us: [sathee@iitk.ac.in](sathee@iitk.ac.in)  \nVisit us at [https://sathee.iitk.ac.in](https://sathee.iitk.ac.in)  \nPage 2 of 4 © 2023-2025 Copyright SATHEE  \nExample 1: Cylinder with a Cone  \n Total Volume = Volume of cylinder + Volume of cone.  \n Formula: 􀟨􀝎2 ℎ + 13􀟨􀝎2 ℎ = 43􀟨􀝎2 ℎ Example 2: Cube with a Hemisphere on Top  \n Total Volume = Volume of cube + Volume of hemisphere.  \n Formula: 􀜽 3 + 23􀟨􀝎3 (where 􀜽 = 2􀝎) Important Points:  \n Step-by-Step Method:  \n Identify the individual solids.  \n Calculate their individual volumes.  \n Add them to get the total volume.  \n Common Mistake: Confusing surface area and volume calculations (e.g. , subtracting areas for volume) .  \nExam-Focused Examples:  \n1. A container is made by joining a cylinder and a hemisphere. Calculate its volume.  \n2. Solution:","cbCaim7nSgfL0RRR","https://ap.wps.com/l/cbCaim7nSgfL0RRR","pdf",239826,"English","# Chapter 12: Surface Areas and Volumes\n## 12.2 Surface Area of a Combination of Solids\n## 12.3 Volume of a Combination of Solids\n## 12.4 Summary","[{\"question\":\"What is TSA (Total Surface Area) for a combination of solids?\",\"answer\":\"TSA is the sum of all outer surfaces. Areas where solids overlap or are in contact are not counted in the total surface area.\"},{\"question\":\"Why do overlapping regions not contribute to surface area calculations?\",\"answer\":\"When two solids are joined, the contact area becomes internal and is not exposed, so it is excluded from TSA.\"},{\"question\":\"What is the main difference between calculating total surface area and total volume?\",\"answer\":\"For surface area, overlapping contact areas must be subtracted. For volume, overlapping regions do not require subtraction—total volume is obtained by adding individual volumes.\"}]","Chapter 12: Surface Areas and Volumes - 12.2 Surface Area of a Combination of Solids | PDF"]