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It then reviews formulas for cuboids, cubes, prisms, cylinders, pyramids, cones, spheres, and hemispheres, and applies them through worked examples involving canvas for a conical tent, painting an oil drum, and computing curved surface area ratios and steel-sheet requirements for hemispherical basins.",{"@graph":14,"@context":77},[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/maths-10-ch10-surface-area-and-volume-of-solids-exercises-and-examples/297475/",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/maths-10-ch10-surface-area-and-volume-of-solids-exercises-and-examples/297475.png","ImageObject",300,407,{"name":42,"@type":43},"McQueen","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69,73],{"name":60,"@type":61,"acceptedAnswer":62},"How do you decide whether to use volume or surface area in a word problem?","Question",{"text":63,"@type":64},"Use surface area when you need paint or material covering an outer surface. Use volume when you need the quantity that occupies space, such as grain inside a container or contents filling a space.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which solids’ formulas are reviewed in the chapter?",{"text":68,"@type":64},"The chapter recalls surface area and volume formulas for cuboid, cube, right prism, right circular cylinder, right pyramid, right circular cone, sphere, and hemisphere.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the slant height of a cone used in calculations?",{"text":72,"@type":64},"The slant height is needed to find the curved surface area of a cone, typically using l = √(r² + h²) before applying πrl.",{"name":74,"@type":61,"acceptedAnswer":75},"What kind of calculations are included in the worked examples?",{"text":76,"@type":64},"The examples compute canvas length for a conical tent, total painting cost for cylindrical drums using total surface area, ratios of curved surface areas of sphere-cylinder-cone with equal dimensions, and required steel-sheet area for manufacturing hemispherical basins.","https://schema.org",{"og:url":32,"og:type":79,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":81,"canonical":32},"index,follow",{"doc_id":83,"site_id":7},297475,1789744834,{"code":4,"msg":86,"data":87},"success",[88,92,96,99,104,109,114,119,124,127,131],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":97,"slug":98},70,"exam",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},5,"Comic",60,"comic",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},6,"Technology",50,"technology",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},7,"Healthcare",40,"healthcare",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},8,"Research & Report",30,"research-report",{"id":120,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":122,"slug":123},9,"Religion & Spirituality",20,"religion-spirituality",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":122,"slug":126},"World Cup","world-cup",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":128,"slug":130},10,"Lifestyle","lifestyle",{"id":132,"doc_module":4,"doc_module_name":25,"category_name":133,"show_sort_weight":100,"slug":134},19,"General","general",{"code":4,"msg":86,"data":136},{"doc_id":83,"user_id":137,"nickname":42,"user_avatar":138,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":139,"file_id":140,"file_url":141,"file_type":142,"file_size":143,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":144,"language":145,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":146,"faqs":147,"seo_title":148,"seo_description":12,"update_tm":84,"read_time":102},5909890329169,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","􀀁􀀂  \n􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀈􀀉􀀊􀀃  \n􀀁􀀂􀀃􀀁 􀀅 􀀆􀀇􀀈􀀉􀀊􀀋􀀌􀀇􀀅􀀉􀀆  \nIn classes VIII and IX, we have learnt about area, surface area and volume of solid shapes. We did many exercises to understand what they mean. We used them in real life situations and identified what we needed and what was tobe measured or estimated. For example, to find the quantity of paint required to whitewash a room, we need the surface area and not the volume. To find the number of boxes that would contains a quantity of grain, we need the volume and not the area.  \n􀀇 􀀈􀀍 􀀇 􀀎􀀅􀀏  \n1. Consider the following situations. In each find out whether you need volume or area and why?  \ni. Quantitiy of water inside a bottle. ii. Canvas needed formaking a tent.  \niii. Number of bags inside the lorry. iv. Gas filled in a cylinder.  \nv. Number of match sticks that can be putin the matchbox.  \n2. Compute 5 more such examples and ask your friends to choose what they need?  \nWe see so manythings of different shapes (combination of two or more) around us. Houses stand on pillars, storage water tanks are cylindrical and are placed on cuboidal foundations, a cricket bathas a cylindrical handle and a flat main body, etc. Think of different things around you. Some of these are shown below:  \n􀀐􀀑􀀒 􀀁􀀂􀀃􀀄􀀄􀀅􀀆 􀀈􀀃􀀉􀀊􀀋􀀌􀀃􀀉􀀍􀀎􀀄  \nOf these objects like football have shapes where we knowthatthe surface area and volume. We can however see that other objects can be seen as combinations ofthe solid shapes. So, their surface area and volume we now have to find. The table of the solid shapes, their areas and volumes are given later.  \n\n| 􀀇 􀀈􀀍 􀀇 􀀎􀀅􀀏 |\n| --- |\n| 1. Break the pictures in the previous figure into solids of known shapes.\u003Cbr>2. Think of 5 more things around you that can be seen as a combination of shapes. Name the shapes that combine to make them. |\n\nLet us recall the surface areas and volumes of different solid shapes.  \n\n| S.\u003Cbr>No. | Name of\u003Cbr>the solid | Figure |  |  |  |  | Lateral / Curved surface area | Total surface\u003Cbr>area | Volume | Nomen\u003Cbr>clature |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1. | Cuboid | l |  |  | h  b  |  | 2h(l+b) | 2(lb+bh+hl) | lbh | l:length\u003Cbr>b:breadth\u003Cbr>h:height |\n| 2. | Cube |  | |  | | a | 4a2 | 6a2 | a3 | a:side of\u003Cbr>the cube |\n|  |  |  |  |  |  |  |  |  |  |  |\n|  |  | \u003Cbr>a |  |  | |  |  |  |  |  |\n|  |  |  |  | a |  |  |  |  |  |  |\n| 3. | Right\u003Cbr>prism | |  |  |  |  | Perimeter of base × height | Lateral surface area+2(area of the end surface) | area of base\u003Cbr>× height | - |\n| 4. | Regular\u003Cbr>circular\u003Cbr>Cylinder | |  |  |  |  | 2πrh | 2πr(r+h) | πr2h | r:radius of\u003Cbr>the base\u003Cbr>h:height |\n| 5. | Right\u003Cbr>pyramid | \u003Cbr>|  |  | |  | ~~12~~ (perimeter of\u003Cbr>base) × slant\u003Cbr>height | Lateral surfaces\u003Cbr>area+area of\u003Cbr>the base | ~~13~~ area of\u003Cbr>the base\u003Cbr>× height | - |\n| 6. | Right\u003Cbr>circular\u003Cbr>cone | |  |  |  |  | πrl | πr(l+r) | ~~13~~ πr2h | r:radius of\u003Cbr>the base\u003Cbr>h:height\u003Cbr>l:slant height |\n| 7. | Sphere | |  |  |  |  | 4πr2 | 4πr2 | ~~43~~ πr3 | r:radius |\n| 8. | Hemisphere |  | |  | |  | 2πr2 | 3πr2 | ~~23~~ πr3 | r:radius |\n|  |  | |  |  |  |  |  |  |  |  |\n\n􀀁􀀂􀀃􀀃 􀀅􀀆􀀇􀀈􀀂􀀆􀀉􀀊􀀈􀀆􀀋􀀌 􀀉􀀍 􀀎􀀏􀀐􀀏 􀀑􀀋􀀒􀀃􀀂􀀌􀀓􀀃􀀌􀀈  \n􀀈􀀋􀀏􀀄􀀐􀀑􀀃􀀉􀀍􀀒􀀏 􀀐􀀑􀀓  \nNow, let us see some examples to illustrate the shapes in the table.  \nExample-1. Theradius ofa conical tent is 7 meters and its height is 10 meters. Calculate the length of canvas used in making the tent if width of canvas is 2m. Use π = 227􀀄􀀉􀀇  \nSolution : If the radius of conical tent is given (r) = 7 metres  \nHeight(h) = 10 m.  \n∴ So, the slant height of the cone l2 = r2 + h2 ⇒ l =  r 2 + h2  \n=  49 + 100  \n= 149 = 12.2 m.  \nNow, Surface area of the tent = πrl  \n= 227 × 7 × 12.2 m2  \n= 268.4 m2.  \nArea of canvas used = 268 .4m2  \nIt is given the width of the canvas = 2m  \n Area 268.4  \nLength of canvas used = = = 134.2m  \nwidth 2  \nExample-2. An oil drum isin the shape of a cylinder having the following dimensions: diameter is 2 m. and height is 7 meters. The painter charges 􀀁3 per m2 to paint the drum. Fi","cbCaiqWHHT0uVmi9","https://ap.wps.com/l/cbCaiqWHHT0uVmi9","pdf",993471,24,"English","# Exercises: Area vs Volume\n## Identifying area or volume in given situations\n## Additional examples and discussion\n# Solid Shapes: Areas and Volumes\n## Cuboid, cube, right prism\n## Cylinder, pyramid, cone\n## Sphere and hemisphere\n# Worked Examples\n## Conical tent canvas length\n## Painting oil drum for multiple units\n## Ratio of curved surface areas (sphere, cylinder, cone)\n## Steel-sheet area for hemispherical basins\n## Right circular cylinder: base, curved, total area, volume","[{\"question\":\"How do you decide whether to use volume or surface area in a word problem?\",\"answer\":\"Use surface area when you need paint or material covering an outer surface. Use volume when you need the quantity that occupies space, such as grain inside a container or contents filling a space.\"},{\"question\":\"Which solids’ formulas are reviewed in the chapter?\",\"answer\":\"The chapter recalls surface area and volume formulas for cuboid, cube, right prism, right circular cylinder, right pyramid, right circular cone, sphere, and hemisphere.\"},{\"question\":\"How is the slant height of a cone used in calculations?\",\"answer\":\"The slant height is needed to find the curved surface area of a cone, typically using l = √(r² + h²) before applying πrl.\"},{\"question\":\"What kind of calculations are included in the worked examples?\",\"answer\":\"The examples compute canvas length for a conical tent, total painting cost for cylindrical drums using total surface area, ratios of curved surface areas of sphere-cylinder-cone with equal dimensions, and required steel-sheet area for manufacturing hemispherical basins.\"}]","Maths-10-CH10 - Surface Area and Volume of Solids - Exercises and Examples | PDF"]