[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297530-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297530-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","lesson-124-real-world-problems-surface-area-and-volume","Lesson 12.4 Real-World Problems: Surface Area and Volume","","Lesson 12.4 focuses on solving real-world word problems involving surface area and volume of prisms. Students calculate the volume of water required for a rectangular fish tank and determine how much additional water is needed for partial filling. The lesson extends to non-rectangular prisms, including prisms with trapezoid or pentagon bases, and square prisms with missing dimensions, using geometric formulas for base area, perimeter, and total surface area.",{"@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/lesson-124-real-world-problems-surface-area-and-volume/297530/",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/lesson-124-real-world-problems-surface-area-and-volume/297530.png","ImageObject",300,407,{"name":42,"@type":43},"Rowan","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you find the volume of water needed to fill a rectangular fish tank?","Question",{"text":63,"@type":64},"Compute the tank’s total volume using length × width × height. Then find how much empty space remains and subtract, yielding the added water volume.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What formulas are used for volume and surface area of a prism in these problems?",{"text":68,"@type":64},"Volume uses V = Bh, where B is base area and h is prism height. Surface area uses perimeter of base × height plus 2 × base area.",{"name":70,"@type":61,"acceptedAnswer":71},"How can you find missing dimensions when only volume is given?",{"text":72,"@type":64},"Use the volume formula V = Bh to solve for the unknown base area or height. For a square base, convert base area into side length, then proceed to surface area with the perimeter-based formula.","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},297530,1789745458,{"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":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},1099514067415,"https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502","12.4   \nReal-World Problems: Surface Area and Volume  \nLesson Objective  \n• Solve problems involving surface area and volume of prisms.  \nrn  \nSolve word problems about the volume of rectangular prisms.  \nA rectangular fish tank 60 centimeters by 15 centimeters by 34 centimeters is ~~ ~~  \n1 3  \nfull of water.  \nFind the volume of water needed to fill the tank completely.  \nVolume of water needed  \n5 Volume of empty space in the tank Height of empty space 5 ~~ ~~  \n2  \n· 34 3  \n5 ~~ ~~  \n68  \ncm  \n3  \nVolume of water needed to fill the tank 5 60 · 15 ·  \n683~~ ~~ Write equation.  \n5 60 · 5 · 68 Divide out common factor 3.  \n5 20,400 cm3 Multiply.  \nTo fill the tank, 20,400 cubic centimeters more water are needed.  \n| |  |  |\n| --- | --- | --- |\n| |  |  |\n\ncm  \n34  \n15 cm  \n60 cm  \na  \ne  \nL  \nGuided Practice  \nComplete.  \n1 Find the volume of water needed to fill three fourths of the aquarium. Height of water needed 5 34 ·  ?   \n5  ?  in.  \nVolume of water needed 5  ?  ·  ?  ·  ?   \n5  ?  in.3  \nThe aquarium needs to have  ?  cubic inches of water added to it to be 34 full.  \n14 in.  \n200 Chapter 12 Surface Area and Volume of Solids  \nrn  Solve word problems about surface area and volume of non-rectangular prisms.  \nA block of wood is a prism and has the dimensions shown in the  \ndiagram below.  \na) Find the volume of the block of wood.  \n3cm  \n4 cm  \n7 cm  \n4 cm  \n3 cm  \nThe base of the prism is a trapezoid.  \nArea of base  \n5 12 h(sum of lengths of parallel sides)  \n5 12 · 3 · (3 1 7)  \n 1  \n5 · 3 · 10 2  \n5 15 cm2  \nVolume  \n5 Bh  \n5 15 · 4  \n5 60 cm3  \nThe volume of the block of wood is 60 cubic centimeters.  \nb) Find the surface area of the wooden block.  \nSurface area of wooden block  \n5 perimeter of base · height 1 total area of two bases  \n5 (7 1 3 1 3 1 5) · 4 1 (2 · 15)  \n5 18 · 4 1 30  \n5 72 1 30  \n5 102 cm2  \nThe surface area of the wooden block is 102 square centimeters.  \na  \ne  \nL  \nLesson 12.4 Real-World Problems: Surface Area and Volume 201  \nGuided Practice  \nComplete.  \n4 cm  \na) Find the volume of the metal bar.  \nArea of parallelogram  \n5 base of parallelogram · height of parallelogram 5  ?  ·  ?   \n5  ?  cm2  \nVolume of metal bar  \n5 base of prism · height of prism 5  ?  ·  ?   \n5  ?  cm3  \nThe volume of the metal bar is  ?  cubic centimeters.  \nb) Find the surface area of the metal bar.  \nSurface area of metal bar  \n5 perimeter of base · height 1 total area of 2 bases 5 ( ?  1  ?  1  ? 1  ? ) ·  ?  1  ?  ·  ?  5  ?  ·  ?  1  ?   \n5  ?  1  ?   \n5  ?  cm2  \nThe surface area of the metal bar is  ?  square centimeters.  \n202 Chapter 12 Surface Area and Volume of Solids  \nrn  Solve word problems about prisms with missing dimensions.  \nA square prism of height 11 inches has a volume of 539 cubic inches.  \na) Find the length of each side of the square base.  \n11 in.  \nV 5 Bh Write formula.  \n539 5 B · 11 Substitute.  \n51319 5 B · 1111 Divide each side by 11.  \n49 5 B Simplify.  \nThe area of the square base is 49 square inches.  \nLength of each side of base 5 49  \n5 7 in.  \nThe length of each side of the square base is 7 inches.  \nb) Find the surface area of the prism.  \nSurface area of prism  \n5 perimeter of base · height 1 area of two bases  \n5 (7 1 7 1 7 1 7) · 11 1 2 · 49  \n5 28 · 11 1 98  \n5 308 1 98  \n5 406 in.2  \nThe surface area of the prism is 406 square inches.  \nTo find the length of the square base, you can first find the area of the square base.  \na  \ne  \nL  \nLesson 12.4 Real-World Problems: Surface Area and Volume 203  \nrn  Solve word problems about non-rectangular prisms with missing dimensions.  \nJacob is making a wooden birdhouse. The birdhouse is a prism  \nwith bases that are pentagons, and has the dimensions shown  \nin the diagram. The volume of the prism is 720 cubic inches.  \n5 in.  \n3 in. 5 in.  \n6 in.  \na) Find the height of the prism.  \nArea of pentagonal base  \n5 area of triangle 1 area of rectangle 5 􀀟􀀞􀀝 12 · 8 · 3􀀜􀀛􀀚 1 8 · 6  \n5 12 1 48  \n5 60 in.2  \nV 5 Bh Write formula.  \n720 5 60 · ","cbCait6Qj8YSw0Dv","https://ap.wps.com/l/cbCait6Qj8YSw0Dv","pdf",1388819,14,"English","# Lesson Objective\n# Real-World Problems: Rectangular Prism Water Volume\n## Guided Practice: Three Fourths of the Aquarium\n# Non-Rectangular Prisms\n## Trapezoid-Based Prism: Volume and Surface Area\n# Guided Practice: Parallelogram/Metal Bar\n## Volume\n## Surface Area\n# Square Prisms With Missing Dimensions\n## Find Side Length\n## Find Surface Area\n# Non-Rectangular Prism With Missing Dimensions\n## Pentagonal Base: Find Height\n## Surface Area","[{\"question\":\"How do you find the volume of water needed to fill a rectangular fish tank?\",\"answer\":\"Compute the tank’s total volume using length × width × height. Then find how much empty space remains and subtract, yielding the added water volume.\"},{\"question\":\"What formulas are used for volume and surface area of a prism in these problems?\",\"answer\":\"Volume uses V = Bh, where B is base area and h is prism height. Surface area uses perimeter of base × height plus 2 × base area.\"},{\"question\":\"How can you find missing dimensions when only volume is given?\",\"answer\":\"Use the volume formula V = Bh to solve for the unknown base area or height. For a square base, convert base area into side length, then proceed to surface area with the perimeter-based formula.\"}]","Lesson 12.4 Real-World Problems: Surface Area and Volume | PDF",35]