[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297389-105":3,"detail-sidebar-cat-0-en-105":73,"doc-detail-297389-en":122},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":66,"head_meta":68,"extra_data":70,"updated_unix":72},105,"en","cbse-class-10-mathematics-surface-areas-and-volumes-worksheet","CBSE - Class 10 Mathematics - Surface Areas and Volumes Worksheet","","CBSE Class 10 Mathematics worksheet on surface areas and volumes with ten geometry problems involving cylinders, cones, hemispheres, spheres, and composite solids. Tasks include finding total surface area after hollowing, calculating areas of toys and capsules, determining maximum hemisphere diameter on a cubical block, inner surface area of a vessel, and volumes of remaining water or mass of an iron pole. Worked solutions show step-by-step radius, height, slant height, formulas, and rounding.",{"@graph":14,"@context":65},[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/cbse-class-10-mathematics-surface-areas-and-volumes-worksheet/297389/",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/cbse-class-10-mathematics-surface-areas-and-volumes-worksheet/297389.png","ImageObject",300,407,{"name":42,"@type":43},"Violet","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59],{"name":60,"@type":61,"acceptedAnswer":62},"What typical steps do the worked solutions follow?","Question",{"text":63,"@type":64},"They identify radii and heights, compute slant height with the Pythagorean theorem, substitute into surface-area formulas, add the required parts, and round the final answer.","Answer","https://schema.org",{"og:url":32,"og:type":67,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":69,"canonical":32},"index,follow",{"doc_id":71,"site_id":7},297389,1789744203,{"code":4,"msg":74,"data":75},"success",[76,80,84,87,92,97,102,107,112,115,119],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":81,"show_sort_weight":82,"slug":83},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":85,"slug":86},70,"exam",{"id":88,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},5,"Comic",60,"comic",{"id":93,"doc_module":4,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},6,"Technology",50,"technology",{"id":98,"doc_module":4,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},7,"Healthcare",40,"healthcare",{"id":103,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},8,"Research & Report",30,"research-report",{"id":108,"doc_module":4,"doc_module_name":25,"category_name":109,"show_sort_weight":110,"slug":111},9,"Religion & Spirituality",20,"religion-spirituality",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":113,"show_sort_weight":110,"slug":114},"World Cup","world-cup",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":116,"slug":118},10,"Lifestyle","lifestyle",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":88,"slug":121},"General","general",{"code":4,"msg":74,"data":123},{"doc_id":71,"user_id":124,"nickname":42,"user_avatar":125,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":55,"language":131,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":12,"update_tm":72,"read_time":135},4398048950312,"https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908","CBSE-Class 10 Mathematics Surface Areas  \nand Volumes Worksheet  \n1. 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 cm$^2$ .  \n2. A toy is in the form of a cone of radius $3.5$ cm mounted on a hemisphere of same radius. The total height of the toy is $15.5$ cm. Find the total surface area of the toy.  \n3. A cubical block of side $7$ cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.  \n4.  \nA medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 12. 10) . The length of the entire capsule is $14$ mm and the diameter of the capsule is $5$ mm. Find its surface area.  \n5. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.  \nDownload the UrbanPro App  \nGet [Free Worksheets on ](Free Worksheets on www.urbanpro.com)[www.urbanpro.com](Free Worksheets on www.urbanpro.com)  \n6. 2 cubes each of volume $64$ cm$^3$ are joined end to end. Find the surface area of the resulting cuboid.  \n7. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14$ cm and the total height of the vessel is $13$  \ncm. Find the inner surface area of the vessel.  \n8. A solid consisting of a right circular cone of height $120$ cm and radius $60$ cm standing on a hemisphere of radius $60$ cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is $60$ cm and its height is $180$ cm.  \n9. A solid iron pole consists of a cylinder of height $220$ cm and base diameter $24$ cm, which is surmounted by another cylinder of height $60$ cm and radius $8$ cm. Find the mass of the pole, given that $1$ cm$^3$ of iron has approximately $8$g mass. (Use $\\pi = 3. 14$)  \n10.A spherical glass vessel has a cylindrical neck $8$ cm long, $2$ cm in diameter; the diameter of the spherical part is $8.5$ cm. By measuring the amount of water it holds, a child finds its volume to be $345$ cm$^3$ . Check whether she is correct, taking the above as the inside measurements, and $\\pi = 3.14$.  \nDownload the UrbanPro App  \nGet [Free Worksheets on ](Free Worksheets on www.urbanpro.com)[www.urbanpro.com](Free Worksheets on www.urbanpro.com)  \nWorksheet Answers  \nSolution:  \nGiven:  \n Height of the cylinder ($h$) = $2.4$ cm  \n Diameter of the cylinder ($d$) = $1.4$ cm  \n Radius of the cylinder ($r$) = $\\frac{d}{2} = \\frac{1 .4}{2} = 0.7$ cm  \n A conical cavity of the same height ($h = 2.4$ cm) and same radius ($r = 0.7$ cm) is hollowed out.  \nTo Find:  \nThe total surface area of the remaining solid, rounded to the nearest cm$^2$ .  \nh=2 .4cm r=0 .7cm  \nStep 1: Identify the components of the Total Surface Area (TSA)  \nWhen a conical cavity is hollowed out from a solid cylinder, the total surface area of the remaining solid consists of:  \n The curved surface area of the cylinder ($2\\pi rh$)  \n The area of the circular base of the cylinder ($\\pi r^2$)  \n The curved surface area of the conical cavity ($\\pi rl$) Formula: $TSA = 2\\pi rh + \\pi r^2 + \\pi rl$  \nStep 2: Calculate the slant height ($l$) of the cone  \nThe slant height $l$ is given by the Pythagorean theorem: $l = \\sqrt{r^2 + h^2}$$l = \\sqrt{(0 .7)^2 + (2 .4)^2}$  \n$l = \\sqrt{0 .49 + 5.76}$  \nDownload the UrbanPro App  \nGet [Free Worksheets on ](Free Worksheets on www.urbanpro.com)[www.urbanpro.com](Free Worksheets on www.urbanpro.com)  \n$l = \\sqrt{6 .25} = 2.5$ cm  \nStep 3: Calculate the individual areas  \nUsing $\\pi \\approx \\frac{22}{7}$:  \nCurved Surface Area of Cylinder = $2 \\times \\frac{22}{7} \\times 0.7 \\times 2.4 = 2 \\times 22 \\times 0","cbCaiqUNvqqQD4Wp","https://ap.wps.com/l/cbCaiqUNvqqQD4Wp","pdf",51847,"English","# Surface Areas and Volumes Worksheet\n## Problems 1-10\n## Worked Solution Example (Problem 1 and 2)","[{\"question\":\"What typical steps do the worked solutions follow?\",\"answer\":\"They identify radii and heights, compute slant height with the Pythagorean theorem, substitute into surface-area formulas, add the required parts, and round the final answer.\"}]","CBSE - Class 10 Mathematics - Surface Areas and Volumes Worksheet | PDF",48]