[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-638278-105":59,"doc-detail-638278-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","surface-area-of-cuboids-3-math-practice-exercises","Surface Area of Cuboids 3 - Math Practice Exercises","","This educational document provides a structured set of math practice exercises focused on calculating the missing side lengths of cuboids given their total surface area. It includes four distinct problems that require students to apply geometric formulas for surface area systematically. Each problem is accompanied by step-by-step solutions, explaining the derivation of missing dimensions through algebraic reasoning and face-area calculations. This resource is designed to help students master volume and surface area concepts for 6th-grade level mathematics, offering both a challenge sheet and a corresponding answer key for self-assessment.",{"@graph":69,"@context":122},[70,84,105],{"@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-cuboids-3-math-practice-exercises/638278/",{"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-cuboids-3-math-practice-exercises/638278.png","ImageObject",300,407,{"name":92,"@type":93},"dawugda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the missing side length of a cuboid if the surface area is known?","Question",{"text":112,"@type":113},"You set up an algebraic equation based on the formula for the total surface area of a cuboid, which involves the sum of the areas of its six faces, and then solve for the unknown side dimension.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the total surface area of the first cuboid in the exercise?",{"text":117,"@type":113},"The first cuboid has a given surface area of 78 cm². Using the provided dimensions of 3 cm by 3 cm for two faces, the calculation reveals the missing side length is 5 cm.",{"name":119,"@type":110,"acceptedAnswer":120},"Why are some faces calculated as pairs in the solutions?",{"text":121,"@type":113},"In a rectangular cuboid, opposite faces are identical in dimensions. Therefore, their areas are the same, allowing for a simplified surface area formula of 2 times the sum of the areas of the three unique face types.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},638278,1792897995,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Name Date  \nSURFACE AREA OF CUBOIDS 3  \nUse the measurements and surface area to find the missing side lengths.  \n| 1) | \u003Cbr> ? cm \u003Cbr>3 cm\u003Cbr> 3 cm | Surface area is 78 cm2 |\n| --- | --- | --- |\n| 2) | ? in Surface area is 158 in2\u003Cbr>|  |\n| 3) 5 in Surface area is 270 in2\u003Cbr>5 in\u003Cbr>? in\u003Cbr>|  |  |\n| 4) ? cm Surface area is 216 cm2 2 cm\u003Cbr>6 cm |  |  |\n\nName Date  \nSURFACE AREA OF CUBOIDS 3 ANSWERS  \n| 1) | \u003Cbr> ? cm \u003Cbr>3 cm\u003Cbr> 3 cm | Surface area is 78 cm2\u003Cbr>Face 1 = ? x 3\u003Cbr>Face 2 = 3 x 3 = 9 cm2 Surface area = ? x 3 x 4 + 9 x 2 = ? x 12 + 18\u003Cbr>So ? x 12 + 18 = 78\u003Cbr>So ? x 12 = 60\u003Cbr>? = 60 ÷ 12 = 5 cm |\n| --- | --- | --- |\n| 2) | ? in\u003Cbr>| Surface area is 158 in2\u003Cbr>Face 1 = ? x 5\u003Cbr>Face 2 = ? x 3\u003Cbr>Face 3 = 3 x 5 = 15 in 2\u003Cbr>Surface area = ? x 5 x 2 + ? x 3 x 2 + 15 x 2 = ? x 10 + ? x 6 + 30 = ? x 16 + 30\u003Cbr>So ? x 16 + 30 = 158\u003Cbr>? = 128 ÷ 16 = 8 cm |\n| 3) 5 in\u003Cbr>5 in\u003Cbr>? in\u003Cbr>|  | Surface area is 270 in2\u003Cbr>Face 1 = ? x 5\u003Cbr>Face 2 = 5 x 5 = 25 in 2\u003Cbr>Surface area = ? x 5 x 4 + 25 x 2 = ? x 20 + 50\u003Cbr>So ? x 20 + 50 = 270\u003Cbr>? = 220 ÷ 20 = 11 in |\n| 4) ? cm\u003Cbr>2 cm\u003Cbr>6 cm |  | Surface area is 216 cm2\u003Cbr>Face 1 = ? x 6\u003Cbr>Face 2 = ? x 2\u003Cbr>Face 3 = 2 x 6 = 12 cm2\u003Cbr>Surface area = ? x 6 x 2 + ? x 2 x 2 + 12 x 2 = ? x 12 + ? x 4 + 24 = ? x 16 + 24\u003Cbr>So ? x 16 + 24 = 216\u003Cbr>? = 192 ÷ 16 = 12 cm |","cbCaismOQRavtX0i","https://ap.wps.com/l/cbCaismOQRavtX0i","pdf",152568,"English","# Practice Problems\n## Surface Area Calculations\n# Answer Key\n## Step-by-Step Solutions","[{\"question\":\"How do you find the missing side length of a cuboid if the surface area is known?\",\"answer\":\"You set up an algebraic equation based on the formula for the total surface area of a cuboid, which involves the sum of the areas of its six faces, and then solve for the unknown side dimension.\"},{\"question\":\"What is the total surface area of the first cuboid in the exercise?\",\"answer\":\"The first cuboid has a given surface area of 78 cm². Using the provided dimensions of 3 cm by 3 cm for two faces, the calculation reveals the missing side length is 5 cm.\"},{\"question\":\"Why are some faces calculated as pairs in the solutions?\",\"answer\":\"In a rectangular cuboid, opposite faces are identical in dimensions. Therefore, their areas are the same, allowing for a simplified surface area formula of 2 times the sum of the areas of the three unique face types.\"}]","Surface Area of Cuboids 3 - Math Practice Exercises | PDF",1792682540]