[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297314-105":59,"doc-detail-297314-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","investigating-the-surface-area-and-volume-of-rectangular-prisms","Investigating the Surface Area and Volume of Rectangular Prisms","","Classroom investigation examining how scaling a rectangular prism affects total surface area (TSA) and volume. Learners work in small groups using identical wooden cubes to measure areas in square units and volumes in cubic units, selecting initial dimensions and applying scale factors of 2, 3, or 4. Results establish consistent volume scaling: k for one dimension, k^2 for two dimensions, and k^3 for all three. Surface-area growth depends on original dimensions for partial scaling, but scales by k^2 when all three dimensions increase.",{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/investigating-the-surface-area-and-volume-of-rectangular-prisms/297314/",{"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/investigating-the-surface-area-and-volume-of-rectangular-prisms/297314.png","ImageObject",300,407,{"name":92,"@type":93},"\tCallum ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-06","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What quantities did learners measure during the investigation?","Question",{"text":113,"@type":114},"Learners measured total surface area in square units and volume in cubic units, using the side length of the wooden cubes as the unit.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the prism’s volume change when one, two, or three dimensions are scaled by k?",{"text":118,"@type":114},"Volume increases by a factor of k when one dimension changes, by k^2 when two dimensions change, and by k^3 when all three dimensions change.",{"name":120,"@type":111,"acceptedAnswer":121},"Why is identifying a pattern for total surface area more difficult than for volume?",{"text":122,"@type":114},"When only one or two dimensions are changed, the TSA increase depends on the specific original dimensions; a clear factor pattern is established only when all three dimensions are increased.","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},297314,1789743783,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"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":19,"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":130,"read_time":52,"preview_page_count":4},137451211410,"https://ap-avatar.wpscdn.com/avatar/2000bb0a9246f588df?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786362646172706240","Investigating the Surface Area and Volume of Rectangular Prisms  \nSenzeni Mbedzi 1 & Duncan Samson 2 1Mary Waters High School, Grahamstown  \n2FRF Mathematics Education Chair, Rhodes University, Grahamstown [1](1mbedzisenzeni@yahoo.com 2d.samson@ru.ac.za)[mbedzisenzeni@yahoo.com](1mbedzisenzeni@yahoo.com 2d.samson@ru.ac.za)[ 2](1mbedzisenzeni@yahoo.com 2d.samson@ru.ac.za)[d.samson@ru.ac.za](1mbedzisenzeni@yahoo.com 2d.samson@ru.ac.za)  \nINTRODUCTION  \nThis paper describes a classroom investigation focusing on surface area and volume of rectangular prisms. The purpose of the activity is to investigate, with respect to the total surface area and volume, the effect of changing one, two or three dimensions of a rectangular prism by a given factor.  \nLearners were divided into small groups, and each group was provided with a pile of identical wooden cubes. Prior to beginning the activity it was agreed upon that areas and volumes would be measured in square units and cubic units respectively, where the unit in question was the side length of the wooden cubes. Each group was then tasked with deciding on the dimensions of their initial rectangular prism which they then built from the wooden cubes. Each group was also provided with a particular scaling factor (2, 3 or 4) as well as a worksheet on which to record their results.  \nBy way of example, let us consider a scaling factor of 2 for an initial rectangular prism with length 3 units, width 2 units, and height 1 unit. The results of the investigation are summarised in Table 1, with the corresponding images shown in Figure 1.  \nTABLE 1: Changing one, two or three dimensions by a factor of 2.  \n\n|  | Figure | Length | Width | Height | TSA | Volume |\n| --- | --- | --- | --- | --- | --- | --- |\n| Original rectangular prism | 1(a) | 3 | 2 | 1 | 22 | 6 |\n|  |  |  |  |  |  |  |\n| 2 x Length | 1(b) | 6 | 2 | 1 | 40 | 12 |\n| 2 x Width | 1(c) | 3 | 4 | 1 | 38 | 12 |\n| 2 x Height | 1(d) | 3 | 2 | 2 | 32 | 12 |\n|  |  |  |  |  |  |  |\n| 2 x (Length & Width) | 1(e) | 6 | 4 | 1 | 68 | 24 |\n| 2 x (Length & Height) | 1(f) | 6 | 2 | 2 | 56 | 24 |\n| 2 x (Width & Height) | 1(g) | 3 | 4 | 2 | 52 | 24 |\n|  |  |  |  |  |  |  |\n| 2 x (Length & Width & Height) | 1(h) | 6 | 4 | 2 | 88 | 48 |\n\nLearning and Teaching Mathematics, No. 15, 2013, pp. 3-6  \n(a)  \n(d)  \n(g)  \n(b) (c)  \n(e)  \n(h)  \n(f)  \n(a) Original rectangular prism  \n(b) 2 x Length  \n(c) 2 x Width  \n(d) 2 x Height  \n(e) 2 x (Length & Width)  \n(f) 2 x (Length & Height)  \n(g) 2 x (Width & Height)  \n(h) 2 x (Length, Width & Height)  \nFIGURE 1: Changing one, two or three dimensions by a factor of 2.  \nAfter completion of the activity the individual groups reported back to the class and a general pattern was established from the results. Individual groups who had a scaling factor of 2 noticed that the volume of the prism increased by (i) a factor of 2 when only one dimension was changed, (ii) a factor of 4 when two dimensions were changed, and (iii) a factor of 8 when all three dimensions were changed. Groups who hada scaling factor of 3 noticed that the volume of the prism increased by (i) a factor of 3 when only one dimension was changed,(ii) a factor of 9 when two dimensions were changed, and (iii) a factor of 27 when all three dimensions were changed. For groups with a scaling factor of 4, the volume increased by a factor of 4, 16 and 64 respectively. From this we were able to establish the more general result, namely that given a scaling factor k , the volume of the original prism increased by (i) a factor of k when only one dimension was changed, (ii) a factor of k 2 when two dimensions were changed, and (iii) a factor of k 3 when all three dimensions were changed.  \nTrying to find a pattern for the total surface area was somewhat more problematic. When only one or two dimensions are changed, the increase in surface area is dependent on the specific length, width and height of the original prism. However, when all three dimensions are increased by","cbCailpnBl9p70Xd","https://ap.wps.com/l/cbCailpnBl9p70Xd","pdf",672329,"English","# Introduction\n# Data and Example (Table 1; Figure 1)\n# Patterns for Volume and Total Surface Area\n# Reflection","[{\"question\":\"What quantities did learners measure during the investigation?\",\"answer\":\"Learners measured total surface area in square units and volume in cubic units, using the side length of the wooden cubes as the unit.\"},{\"question\":\"How does the prism’s volume change when one, two, or three dimensions are scaled by k?\",\"answer\":\"Volume increases by a factor of k when one dimension changes, by k^2 when two dimensions change, and by k^3 when all three dimensions change.\"},{\"question\":\"Why is identifying a pattern for total surface area more difficult than for volume?\",\"answer\":\"When only one or two dimensions are changed, the TSA increase depends on the specific original dimensions; a clear factor pattern is established only when all three dimensions are increased.\"}]","Investigating the Surface Area and Volume of Rectangular Prisms | PDF"]