[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297510-105":59,"doc-detail-297510-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","surface-area-of-frustums-practice-questions","Surface Area of Frustums - Practice Questions","","A set of practice questions focused on calculating the total surface area of frustums formed by removing the top of shapes such as square-based pyramids and cones using planes parallel to the base. The problems specify large and small base dimensions or radii/diameters, along with slant heights for the corresponding frustum faces. Learners compute surface areas under different answer requirements, including exact forms in terms of π and numerical rounding to specified decimal places or the nearest square centimetre. One challenge problem asks for an unknown dimension using a given total surface area.",{"@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/surface-area-of-frustums-practice-questions/297510/",{"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/surface-area-of-frustums-practice-questions/297510.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the total surface area of a frustum of a square-based pyramid?","Question",{"text":113,"@type":114},"Add the areas of the four trapezoidal faces (or equivalently the areas derived from the frustum’s slant height and the difference between the large and small base side lengths) to get the total surface area.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"When a question says “Give your answer in terms of π,” what should be used?",{"text":118,"@type":114},"Use π in the final expression for any circular sector or circle-related curved surface area, rather than substituting an approximate value for π.",{"name":120,"@type":111,"acceptedAnswer":121},"What information is needed for cone frustum surface area calculations?",{"text":122,"@type":114},"You need the large and small radii (or diameters) and the corresponding slant heights for the frustum’s curved surface, then apply the curved surface area formula and include any required rounding format specified.","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},297510,1790340313,{"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":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","| 1) A frustum is formed by removing the top of a square-based pyramid that was cut parallel to the base. The dimensions are as follows:\u003Cbr>• Large square base side length = 24 cm\u003Cbr>• Small square top side length = 12 cm\u003Cbr>• Height of each large triangular face = 20 cm\u003Cbr>• Height of each small triangular face = 10 cm Calculate the total surface area of the frustum.\u003Cbr>\u003Cbr>\u003Cbr>| 2) A frustum is formed by removing the top of a square-based pyramid that was cut parallel to the base. The dimensions are as follows:\u003Cbr>• Large square base side length = 30 cm\u003Cbr>• Small square top side length = 18 cm\u003Cbr>• Height of each large triangular face = 25 cm\u003Cbr>• Height of each small triangular face = 15 cm Calculate the total surface area of the frustum.\u003Cbr>\u003Cbr>|\n| --- | --- |\n\n\n| 3) A frustum is formed by removing the top of a square-based pyramid that was cut parallel to the base. The dimensions are as follows:\u003Cbr>• Large square base side length = 35 cm\u003Cbr>• Height of each large triangular face = 30 cm\u003Cbr>• Height of each small triangular face = 12 cm Calculate the total surface area of the frustum.\u003Cbr>\u003Cbr>| 4) A frustum is formed by removing the top of a cone. The dimensions are as follows:\u003Cbr>• Large radius = 12 cm\u003Cbr>• Small radius = 6 cm\u003Cbr>• Large slant height = 20 cm\u003Cbr>• Small slant height = 10 cm\u003Cbr>Calculate the total surface area of the frustum.\u003Cbr>Give your answer in terms of π.\u003Cbr>\u003Cbr>|\n| --- | --- |\n\n\n| 5) A frustum is formed by removing the top of a cone. The dimensions are as follows:\u003Cbr>• Large diameter = 30 mm\u003Cbr>• Small diameter = 18 mm\u003Cbr>• Large slant height = 25 mm\u003Cbr>• Small slant height = 15 mm Calculate the total surface area of the frustum.\u003Cbr>Give your answer to 1 decimal place.\u003Cbr>\u003Cbr>| 6) A frustum is formed by removing the top of a cone using a plane parallel to the base. The dimensions are as follows:\u003Cbr>• Large radius = 12 cm\u003Cbr>• Small radius = 8 cm\u003Cbr>• Small slant height = 14 cm\u003Cbr>Calculate the total surface area of the frustum.\u003Cbr>Give your answer to the nearest square centimetre.\u003Cbr>\u003Cbr>|\n| --- | --- |\n\n\n| 7) A cone has a radius of 8 cm and a perpendicular height of 15 cm. A frustum is formed by removing the top of the cone using a plane parallel to the base.\u003Cbr>The smaller cone has a radius of 4 cm.\u003Cbr>Work out the total surface area of the frustum.\u003Cbr>Give your answer to 2 decimal places.\u003Cbr>\u003Cbr>| Challenge\u003Cbr>8) The frustum of a square-based pyramid has a slant height of 10 cm, a top side length of 􀝔 cm and a bottom side length of 2􀝔 cm. The total surface area of the frustum is 320 cm2.\u003Cbr>Work out the value of 􀝔 .\u003Cbr>\u003Cbr>|\n| --- | --- |\n\n\n| 9) A square-based pyramid has slant height ℎ cm and base side length (2􀜽) cm.\u003Cbr>The top third of the pyramid is removed by a plane parallel to the base.\u003Cbr>Show that the total surface area of the remaining frustumis (􀫝􀫙􀫢 􀢇􀫛 + 􀫜􀫛􀫢 􀢇􀢎) cm2.\u003Cbr>\u003Cbr>| 10) A cone has a slant height of 3ℎ and a radius of 2􀝎 .\u003Cbr>A frustum is formed by removing the top of a cone that was cut by a plane parallel to the base.\u003Cbr>The small cone has a slant height of ℎ .\u003Cbr>Work out the total surface area of the frustum.\u003Cbr>Give your answer in terms of π, 􀝎 and ℎ .\u003Cbr>\u003Cbr>|\n| --- | --- |","cbCaiqdy86s4acdk","https://ap.wps.com/l/cbCaiqdy86s4acdk","pdf",309439,"English","# Calculate Total Surface Area of Frustums\n## Square-Based Pyramid Frustums\n## Cone Frustums (Using Slant Height)\n## Mixed/Challenge Problems","[{\"question\":\"How do you find the total surface area of a frustum of a square-based pyramid?\",\"answer\":\"Add the areas of the four trapezoidal faces (or equivalently the areas derived from the frustum’s slant height and the difference between the large and small base side lengths) to get the total surface area.\"},{\"question\":\"When a question says “Give your answer in terms of π,” what should be used?\",\"answer\":\"Use π in the final expression for any circular sector or circle-related curved surface area, rather than substituting an approximate value for π.\"},{\"question\":\"What information is needed for cone frustum surface area calculations?\",\"answer\":\"You need the large and small radii (or diameters) and the corresponding slant heights for the frustum’s curved surface, then apply the curved surface area formula and include any required rounding format specified.\"}]","Surface Area of Frustums - Practice Questions | PDF",1789745227,13]