[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297262-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297262-en":130},{"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","area-of-solid-shapes-surface-area-formulas-and-examples","Area of Solid Shapes - Surface Area Formulas and Examples","","Area of solid shapes covers surface area calculations for common 3D figures: cube, cuboid, cone, prism, pyramid, and frustum of a cone. It provides key surface area formulas such as SA for cube and cuboid, CSA and TSA for cone, prism surface area based on base area and perimeter, and pyramid surface area from the base and triangular faces. Worked examples use given measurements, followed by class activities, evaluation problems, and an assignment set for practice.",{"@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/area-of-solid-shapes-surface-area-formulas-and-examples/297262/",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/area-of-solid-shapes-surface-area-formulas-and-examples/297262.png","ImageObject",300,407,{"name":42,"@type":43},"Aria","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the surface area formula for a cube and how is it used in the example?","Question",{"text":63,"@type":64},"A cube has surface area SA = 6a². The example substitutes a = 5 cm to get SA = 6 × 5² = 150 cm².","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you calculate the curved and total surface area of a cone?",{"text":68,"@type":64},"For a cone, curved surface area is CSA = πrl and total surface area is TSA = πrl + πr². The example uses π = 22/7 with r = 7 cm and l = 24 cm.",{"name":70,"@type":61,"acceptedAnswer":71},"How is the surface area of a frustum of a cone determined?",{"text":72,"@type":64},"For a frustum, CSA = π(R + r)l and TSA = π(R + r)l + πR² + πr². The example computes TSA by adding CSA to the areas of the two circular ends using π = 22/7.","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},297262,1789743411,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":101,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":143},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","AREA OF SOLID SHAPES  \nCUBE  \nA cube has all six faces as squares of side a.  \nSurface area of a cube:  \nSA = 6a²  \nExample 1  \nFind the surface area of a cube with side 5 cm.  \nSolution:  \nSA = 6 × 5² = 6 × 25 = 150 cm²  \n2. CUBOID  \nA cuboid has length l, breadth b, and height h.  \nSurface area of a cuboid:  \nSA = 2(lb + bh + hl)  \nExample 2  \nFind the surface area of a cuboid with length 8 cm, breadth 5 cm, height 3 cm.  \nSolution:  \nSA = 2(8×5 + 5×3 + 8×3)  \n= 2(40 + 15 + 24)  \n= 2 × 79 = 158 cm²  \n3. CONE  \nA cone has radius r and slant height l.  \nCurved surface area (CSA) = πrl  \nTotal surface area (TSA) = πrl + πr²  \nExample 3  \nFind the total surface area of a cone with radius 7 cm and slant height 24 cm (π = 22/7) .  \nSolution:  \nTSA = πrl + πr²  \n= 22/7 × 7 × 24 + 22/7 × 7²  \n= 22 × 24 + 22 × 7  \n= 528 + 154 = 682 cm²  \n4. PRISM  \nA prism has two identical polygonal bases and rectangular sides.  \nSurface area of a prism:  \nSA = 2 × area of base + perimeter of base × height  \nExample 4  \nA triangular prism has base area 24 cm², perimeter of base 18 cm, and height 10 cm. Find SA.  \nSolution:  \nSA = 2 × 24 + 18 × 10  \n= 48 + 180 = 228 cm²  \n5. PYRAMID  \nA pyramid has a polygonal base and triangular faces meeting at a vertex.  \nSurface area:  \nSA = Area of base + sum of areas of triangular faces  \nExample 5  \nA square pyramid has base 6 cm × 6 cm, slant height 5 cm. Find SA.  \nSolution:  \nArea of base = 6 × 6 = 36 cm²  \nArea of 4 triangles = 4 × (1/2 × base × slant height)= 4 × 1/2 × 6 × 5 = 4 × 15 = 60 cm²  \nTSA = 36 + 60 = 96 cm²  \n6. FRUSTUM OF A CONE  \nA frustum is a cone with the top cut off. Let R = radius of larger base, r = radius of smaller base, l = slant height.  \nCurved surface area (CSA) = π(R + r)l  \nTotal surface area (TSA) = π(R + r)l + πR² + πr²  \nExample 6  \nFind the TSA of a frustum with R = 14 cm, r = 7 cm, l = 10 cm (π = 22/7) .  \nSolution:  \nCSA = π(R + r)l = 22/7 × (14 + 7) × 10 = 22/7 × 21 × 10 = 22 × 30 = 660 cm²  \nTSA = 660 + πR² + πr² = 660 + 22/7 × 196 + 22/7 × 49 = 660 + 616 + 154 = 1430 cm²  \nCLASS ACTIVITIES  \nActivity 1 – Model Observation  \nStudents identify and list the faces of a cube, cuboid, prism, pyramid, cone, frustum.  \nActivity 2 – Group Calculation  \nEach group calculates surface area of a solid:  \nCube: side 8 cm  \nCuboid: 5 × 6 × 7 cm  \nCone: radius 7 cm, slant height 24 cm  \nPrism: triangular base 12 cm², perimeter 18 cm, height 10 cm  \nPyramid: square base 4 × 4 cm, slant height 3 cm  \nFrustum: R = 10 cm, r = 6 cm, l = 8 cm  \nGroups present solutions.  \nEVALUATION / CLASSWORK  \nFind the surface area of a cube of side 9 cm.  \nFind the surface area of a cuboid of length 10 cm, breadth 5 cm, height 4 cm.  \nA cone has radius 7 cm and slant height 24 cm. Find the curved and total surface area.  \nA triangular prism has base area 20 cm², perimeter 18 cm, height 15 cm. Find SA.  \nFind the TSA of a square pyramid with base 5 × 5 cm, slant height 6 cm.  \nFind the TSA of a frustum with R = 12 cm, r = 6 cm, l = 10 cm.  \nASSIGNMENT  \nCube of side 10 cm: find TSA  \nCuboid: 8 × 6 × 4 cm: find TSA  \nCone: radius 7 cm, slant height 15 cm: find TSA  \nPyramid: base 6 × 6 cm, slant height 10 cm: find TSA  \nFrustum: R = 14 cm, r = 7 cm, l = 12 cm: find TSA","cbCaigL6Fm8Mg0dp","https://ap.wps.com/l/cbCaigL6Fm8Mg0dp","pdf",65248,"English","# Area of Solid Shapes\n## Cube\n## Cuboid\n## Cone\n## Prism\n## Pyramid\n## Frustum of a Cone\n## Class Activities\n## Evaluation / Classwork\n## Assignment","[{\"question\":\"What is the surface area formula for a cube and how is it used in the example?\",\"answer\":\"A cube has surface area SA = 6a². The example substitutes a = 5 cm to get SA = 6 × 5² = 150 cm².\"},{\"question\":\"How do you calculate the curved and total surface area of a cone?\",\"answer\":\"For a cone, curved surface area is CSA = πrl and total surface area is TSA = πrl + πr². The example uses π = 22/7 with r = 7 cm and l = 24 cm.\"},{\"question\":\"How is the surface area of a frustum of a cone determined?\",\"answer\":\"For a frustum, CSA = π(R + r)l and TSA = π(R + r)l + πR² + πr². The example computes TSA by adding CSA to the areas of the two circular ends using π = 22/7.\"}]","Area of Solid Shapes - Surface Area Formulas and Examples | PDF",15]