[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297539-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297539-en":131},{"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":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","practice-paper-1-geometry-surface-area-and-volume","Practice Paper 1 - Geometry - Surface Area and Volume","","Practice paper focused on geometry problems covering surface area and volume of 3D solids including spheres, cylinders, cones, cubes, cuboids, hemispheres, and composite shapes. It includes compulsory MCQs, very short answers, assertion–reason questions, and multi-mark calculation tasks with given radii, diameters, heights, slant heights, and thicknesses. A case study on a cylindrical water tank with a hemispherical dome requires volume, total surface area, and painting cost, plus the curved-surface formula.",{"@graph":14,"@context":73},[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/practice-paper-1-geometry-surface-area-and-volume/297539/",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/practice-paper-1-geometry-surface-area-and-volume/297539.png","ImageObject",300,407,{"name":42,"@type":43},"Theodora","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",21,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"Which topics of 3D shapes are included in the practice paper?","Question",{"text":63,"@type":64},"The paper covers spheres, cylinders, cones, cubes, cuboids, hollow hemispheres, and a composite water-tank case with a hemispherical dome.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you determine the volume when radii and heights are given?",{"text":68,"@type":64},"Use the corresponding solid’s volume formula (e.g., for a sphere and for a cylinder) and substitute the given dimensions directly.",{"name":70,"@type":61,"acceptedAnswer":71},"What information is needed to compute the cost of painting in the case study?",{"text":72,"@type":64},"You need the total surface area of the tank/dome combination, along with the painting rate (Rs. 15 per m²).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297539,1790161100,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":101,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},687197207919,"https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552","GENERAL INSTRUCTIONS  \n1. All questions are compulsory unless stated otherwise.  \n2. Use neat and clean working.  \n3. Figures to the right indicate full marks.  \n4. Attempt questions in sequence.  \n5. Use proper formulas wherever required.  \nPART – A  \nSECTION I (1 × 6 = 6 Marks)  \n1. MCQ: The surface area of a sphere is 154 cm² . Its radius is:  \na) 3.5 cm b) 7 cm c) 3 cm d) 12.25 cm  \n2. MCQ: If the radius of a cylinder is doubled and the height is also doubled, the volume becomes:  \na) 2 times b) 4 times c) 8 times d) 16 times  \n3. Write the formula for the total surface area of a cone.  \n4. Assertion–Reason (1 mark):  \nAssertion (A): The curved surface area of a cylinder is independent of its volume.  \nReason (R): Curved surface area = 2πrh.  \na) Both A and R are true and R is the correct explanation of A  \nb) Both A and R are true, but R is not the correct explanation of A  \nc) A is true, but R is false  \nd) A is false, but R is true  \n5. Very Short Answer: Define lateral surface area.  \n6. State the formula for the volume of a sphere.  \nPART – B  \nSECTION II (2 × 5 = 10 Marks)  \n7. A cylinder has radius 7 cm and height 10 cm. Find its curved surface area.  \n8. The radius of a sphere is 6 cm. Find its volume.  \n9. Find the total surface area of a cube whose edge is 8 cm.  \n10. A cone has radius 3.5 cm and slant height 6 cm. Find its curved surface area.  \n11. A solid sphere of radius 7 cm is melted to form smaller spheres of radius 1 cm each. Find the number of smaller spheres.  \nSECTION III (3 × 4 = 12 Marks)  \n12. A metallic cuboid of dimensions 12 cm × 10 cm × 8 cm is melted and recast into cylindrical rods of radius 4 cm. Find the height of each rod.  \n13. The diameters of two spheres are in the ratio 3:4 . Find the ratio of their volumes.  \n14. The radius and height of a cone are in the ratio 3:4 . If the slant height is 25 cm, find the radius and height.  \n15. A hollow hemisphere has inner radius 7 cm and thickness 1 cm. Find its total surface area.  \nSECTION IV (5 × 1 = 5 Marks)  \n16. A solid cylinder of radius 7 cm and height 15 cm is cut into two equal parts along its height. Find the total surface area of each part.  \nSECTION V – CASE STUDY BASED QUESTION (1 × 7 = 7 Marks)  \nCase Study:  \nA water tank is in the shape of a cylinder of radius 3 m and height 5 m. It is closed with a dome-shaped hemispherical roof of radius 3 m.  \nAnswer the following:  \na) Find the volume of water the tank can hold. (2)  \nb) Find the total surface area of the tank. (2)  \nc) If the tank is painted at Rs. 15 per m², find the cost of painting. (2)  \nd) Name the formula used for the curved surface area of the dome. (1)  \nEND OF QUESTION PAPER  \nANSWER KEY / MARKING SCHEME  \nPART – A : SECTION I (1 × 6 = 6 Marks)  \n1. Answer: a) 3.5 cm  \nSolution:  \nSurface area of sphere (􀜵 = 4􀟨 􀝎 2 = 154)  \n4 × 227 × 􀝎 2 = 154  \n􀝎 2 = 154~~ ~~×227 = 12.25  \n􀝎 = 3.5  \nAnswer: c) 8 times  \nSolution: Volume of cylinder (􀜸 = 􀟨 􀝎 2 ℎ)  \nIf r → 2r and h → 2h: 􀜸􀯡􀯘􀯪 = 􀟨 (2􀝎)2 (2ℎ) = 8 􀟨 􀝎 2 ℎ = 8 􀜸  \n3. Answer: Formula for total surface area of a cone: 􀜶􀜵􀜣 = 􀟨 􀝎(􀝈 + 􀝎)  \n4. Answer: a) Both A and R are true, and R is the correct explanation of A  \nReasoning: Curved surface area of a cylinder = (2\\pi rh) does not involve volume ((\\pi r^2 h)), so CSA is independent of volume.  \n5. Answer: Lateral surface area is the area of the curved surface of a 3D figure excluding base(s) .  \n6. Answer: Volume of a sphere: 􀜸 = 43 􀟨 􀝎 3  \nPART – B : SECTION II (2 × 5 = 10 Marks)  \n7. Curved Surface Area of Cylinder: (􀜥􀜵􀜣 = 2􀟨 􀝎ℎ) r = 7, h = 10  \n􀜥􀜵􀜣 = 2 × 227 × 7 × 10 = 440 􀜿􀝉²  \n8. Volume of Sphere:  \n􀜸 = 43 􀟨 􀝎 3,  \n􀝎 = 6  \n􀜸 = 4 × 22 × 63 = 4 × 22 × 216 = 904 32 􀜿􀝉 ³ 3 7 3 7 .  \n9. Total Surface Area of Cube: (TSA = 6a2) a = 8  \nTSA = 6 x 64 = 384 cm²  \n10. Curved Surface Area of Cone: (􀜥􀜵􀜣 = 􀟨 􀝎 􀝈) r = 3.5, l = 6  \n􀜥􀜵􀜣 = 227 × 3.5 × 6 = 66 􀜿􀝉²  \n11. Number of smaller spheres:􀜸􀯟􀯔􀯥􀯚􀯘 = 43 􀟨 73 = 43 􀟨 343 = 13732 􀟨􀜸􀯦􀯠􀯔􀯟􀯟 = 43 􀟨 13 = 43  􀟨  \n􀝊 = 􀜸􀜸􀯟􀯦􀯔􀯥􀯠􀯚􀯔􀯟􀯘􀯟~~ ~~ = 137~~3~~432","cbCaivV3IySJ7BI8","https://ap.wps.com/l/cbCaivV3IySJ7BI8","pdf",431867,"English","# PART – A\n## SECTION I\n## PART – B\n## SECTION II\n## SECTION III\n## SECTION IV\n## SECTION V – CASE STUDY BASED QUESTION","[{\"question\":\"Which topics of 3D shapes are included in the practice paper?\",\"answer\":\"The paper covers spheres, cylinders, cones, cubes, cuboids, hollow hemispheres, and a composite water-tank case with a hemispherical dome.\"},{\"question\":\"How do you determine the volume when radii and heights are given?\",\"answer\":\"Use the corresponding solid’s volume formula (e.g., for a sphere and for a cylinder) and substitute the given dimensions directly.\"},{\"question\":\"What information is needed to compute the cost of painting in the case study?\",\"answer\":\"You need the total surface area of the tank/dome combination, along with the painting rate (Rs. 15 per m²).\"}]","Practice Paper 1 - Geometry - Surface Area and Volume | PDF",1789745562,15]