[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297540-105":59,"doc-detail-297540-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","mensuration-chapter-16-archimedes-of-syracuse","Mensuration - Chapter 16 - Archimedes of Syracuse","","Chapter 16 in Mensuration introduces cylinder, cone, frustum of a cone, sphere, and hemisphere with focus on meanings, properties, and measurements. The unit develops formulas to calculate surface area and volume, including LSA/CSA and TSA, and applies them to real-life problems such as overhead water tanks and cylindrical fuel storage. It also covers combined solids, scale drawings for irregular figures, and identifying objects made from two or more solids.",{"@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/mensuration-chapter-16-archimedes-of-syracuse/297540/",{"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/mensuration-chapter-16-archimedes-of-syracuse/297540.png","ImageObject",300,407,{"name":92,"@type":93},"Genevieve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","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},"What does this unit cover under Mensuration?","Question",{"text":113,"@type":114},"It defines cylinder, cone, frustum of a cone, sphere, and hemisphere, then guides calculation of surface area and volume and their lateral/total surface areas. It also includes combined figures, scale drawings, and application problems based on area and volume.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you find the height of a cylinder in the given activity?",{"text":118,"@type":114},"Place a cylinder on the table and hold cardboard parallel to the top, touching the top of the cylinder. The perpendicular distance from the top of the table (bottom of the cylinder) to the cardboard (top of the cylinder) is the cylinder’s height.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the difference between LSA and TSA for a solid cylinder?",{"text":122,"@type":114},"LSA/CSA refers to the curved surface area only. TSA is the sum of areas of the two circular base regions and the curved surface area.","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},297540,1789745565,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},1374391974585,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Meaning of cylinder, cone, frustum of a cone, sphere and hemisphere .  \n Surface area and volume of cylinder, cone, frustum of acone, sphere and hemisphere .  \n Combined figures, their area and volume .  \n Scale drawing.  \n16  \nArchimedes  \n(287BC-212BC)  \nArchimedes ofsyracuse, Sicily, is remembered as the greatest Greek mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas and volumes of solid objects. He proved that the volume of a sphere is equal to two-thirds the volume of a circumscribed cylinder.  \nMensuration  \nThis unit facilitates you in,  \n defining cylinder, cone and sphere .  \n explaining the properties of cylinder, cone and sphere and hemisphere .  \n deriving the formula to find the area and volume of cylinder, cone, sphere and hemisphere .  \n calculating the LSA and TSA of cylinder, cone, sphere and hemisphere .  \n calculating the volume of cylinder, cone, sphere and hemisphere .  \n solving application problems based on area and volume of cylinder, cone and sphere .  \n explaining the meaning offrustum ofa cone .  \n calculating the area and volume of frustum of a cone .  \n identifying objects made up of two or more solids.  \n finding the area and volume of combined solid objects.  \n constructing scale drawing for irregular shaped figures.  \n calcualting area of irregular shaped figures.  \nGive me a place to stand, and I will move the earth.  \n-Archimedes of Syracuse  \nThe study of measurement of objects is very essential because of its applications in  \nevery day life, industry and engineering. We have already learnt to find the surface area and volume of solid objects such as cube, cuboid, prism and pyramid.  \nNow let us consider some examples where measurement of objects are applied.  \n• A village panchayat has built an over head water storage tank which is cylindrical in shape. How to determine the size of the tank? What  \nis the cost incurred in painting the tank?  \n• How do you calculate the amount of diesel that can be stored in a cylindrical shaped fuel tank of a truck?  \n•  \n• How many basin laddoos can be made from  \nWhat is the quantity colour paper required prepare a birthday cap?  \ngiven weight of mixture  \nof  \nto  \nof basin laddoo?  \nThe solution for all the above mentioned problems depends on finding the surface area and volume of solid objects like cylinder, cone and sphere .  \nHow to find the surface area and volume of these objects? Which are the formulae used?  \nIn this unit, let us learn about the surface area and volume of cylinder, cone and sphere .  \nCylinder  \nWe have studied that when a number of rectangular sheets of paper are stacked up, we get a cuboid or rectangular based prism.   \nWhat do we get when a number of congruent circular sheets of paper are stacked up?  \nObserve the figures given.  \nThe solid object obtained is called Cylinder.  \n􀀿 Cylinders are sort of prisms with circular bases.  \nActivity: Take a thick paper and cut a rectangle ABCD. Paste a long thick stick along one side, say AB. Hold the stick with both your palms and rotate it fast (you can also paste a  \nlong thick string, hold the string with hands, on either side and rotate it fast) .  \nDo this activity in groups. Discuss and share the ideas.  \nWhat shape can you recognise? From the above activity, we can conclude that  \nIf a rectangle revolves about one of its sides and completes a full rotation, the solid formed is called a right circular cylinder.  \nIn our daily life, we have seen many objects which are cylindrical in shape. Some of them are given below.  \nThe cylinders can be either solid or hollow . Observe that the cylinder has two circular bases,  \nMilk can Pipe Gas cylinder Pillars  \nbottom base and top base which are congruent to each other.  \nActivity: Place a cylinder on the table and hold a piece of cardboard parallel to the top of the table and touching the top of the cylinder.  \nIf we find the perpendicular distance between the t","cbCail40zeLIJwtO","https://ap.wps.com/l/cbCail40zeLIJwtO","pdf",4101732,38,"English","# Mensuration\n## Archimedes of Syracuse\n## Unit scope and learning outcomes\n## Cylinder: definition and properties\n### Solid and hollow cylinders\n### Height, bases, and axis\n## Surface area of a cylinder\n## Lateral surface area (LSA/CSA)\n## Total surface area (TSA)","[{\"question\":\"What does this unit cover under Mensuration?\",\"answer\":\"It defines cylinder, cone, frustum of a cone, sphere, and hemisphere, then guides calculation of surface area and volume and their lateral/total surface areas. It also includes combined figures, scale drawings, and application problems based on area and volume.\"},{\"question\":\"How do you find the height of a cylinder in the given activity?\",\"answer\":\"Place a cylinder on the table and hold cardboard parallel to the top, touching the top of the cylinder. The perpendicular distance from the top of the table (bottom of the cylinder) to the cardboard (top of the cylinder) is the cylinder’s height.\"},{\"question\":\"What is the difference between LSA and TSA for a solid cylinder?\",\"answer\":\"LSA/CSA refers to the curved surface area only. TSA is the sum of areas of the two circular base regions and the curved surface area.\"}]","Mensuration - Chapter 16 - Archimedes of Syracuse | PDF",96]