[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297253-105":59,"doc-detail-297253-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","prisms-cylinders-measurement","Prisms-Cylinders - Measurement","","Measurement guide focused on 3-D shapes, especially prisms and cylinders, covering key geometry ideas and applying formulas to real dimensions. It recaps surface area and volume concepts, derives total surface area for right prisms and cylinders using length, breadth, height, radius, and slant/curved-surface relationships. Worked examples calculate TSA and volume for both closed and open cases, followed by practice exercises requiring surface area and volume for multiple prism and cylinder configurations.",{"@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/prisms-cylinders-measurement/297253/",{"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/prisms-cylinders-measurement/297253.png","ImageObject",300,407,{"name":92,"@type":93},"Olivia Brown","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the total surface area formula for a closed rectangular prism?","Question",{"text":113,"@type":114},"Total surface area is TSA = 2LB + 2LH + 2BH, using length (L), breadth (B), and height (H).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the surface area of a prism change when it is open on top?",{"text":118,"@type":114},"An open-top prism is missing the top panel, so the surface area uses LB + 2LH + 2BH (top missing).",{"name":120,"@type":111,"acceptedAnswer":121},"How are the formulas for cylinder volume and surface area expressed using radius and height?",{"text":122,"@type":114},"Cylinder volume is V = πr²h, and total surface area is given using πr² and the curved-surface term involving πrh, adjusted for whether the cylinder is closed or open-topped.","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},297253,1789743381,{"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":44,"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":144},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","MEASUREMENT  \n• Recap: Measurement Concepts  \n• Prisms  \n• Cylinders  \n• Scale Factors  \n• Spheres  \n• Pyramids  \n• Cones  \n  Recap: Perimeter and Area   Building a 3-D Space   \n1  \nRECAP: MEASUREMENT  \nCONCEPTS  \n  Recap: Perimeter and Area    Building a 3-D Space   \nPRISMS  \nTotal Surface Area  \nTSA = (L x B) + (L x B) + (L x H) + (L x H) + (B x H) + (B x H)= 2LB + 2LH + 2BH  \n􀂄 Sum the areas of the panels of the rectangle to get the total surface area  \nVolume  \n= (L x B x H)  \nExample  \n(a) Calculate the surface area and volume of the rectangular prism if it is closed on all sides. l = 8cm; b = 3cm ; h = 4cm  \nSurface Area = 2LB + 2LH + 2BH  \nSurface Area = 2(8) (3) + 2(8) (4) + 2(3) (4)  \nSurface Area = 48+64+24  \nSurface Area = 136 cm²  \n(b) Calculate the surface area if the prism is open on top.  \nSurface Area = LB + 2LH + 2BH (TOP MISSING)  \nSurface Area = (8) (3) + 2(8) (4) + 2(3) (4) Surface Area = 112 cm²  \n  Challenge! Diagonal Length of a Rectangular Prism   \nVolume & Surface Area of a Right Prism  \n4  \nEXERCISE  \nCalculate the surface area and volume of a rectangular prism in each of the following cases.  \n(a) the prism is closed and the dimensions are: Length = 13 cm. Breadth = 6 cm and Height = 9 cm  \n(b) the prism is closed and the dimensions are:  \nLength = 12 m, Breadth = 5 m and Height = 7 m  \n(c) the prism is open on top and the dimensions are: Length = 13 cm, Breadth = 6 cm and Height = 9 cm  \n(d) the prism is open on top and the dimensions are: Length = 12 m, Breadth = 5 m and Height = 1 m  \n Volume of Triangular Prisms   \n5  \nCYLINDERS  \nThe Radius of a Circle  Circumference of a Circle  \nTotal Surface Area  \nTSA 􀀠 2􀁓r2 􀀎 2􀁓rh  \nA Cylinder & its Net  \nProof: Curved Surface of a Cylinder = Rectangle  \nVolume  \nV 􀀠 􀁓r2 􀁵 h  \nVolume & Surface Area of a Cylinder Example  \nCalculate the Surface Area & Volume of Cylinders  \nExample  \nGiven a cylinder with r = 4cm and h = 6m:  \n􀂄 (a) Calculate the surface area of the cylinder assuming a closed cylinder  \nTSA  \nTSA  \nTSA  \n􀀠 2􀁓r 2 􀀎 2􀁓rh  \n􀀠 32 􀁓 􀀎 48 􀁓  \n􀀠 (80􀁓 )cm 2  \n􀂄 (b) Calculate the surface area of the cylinder  \nassuming an open-topped cylinder  \nTSA  \nTSA  \nTSA  \nTSA  \n􀀠 􀁓r 2 􀀎 2􀁓rh  \n􀀠 􀁓 (4)2 􀀎 2􀁓 (4)(6)  \n􀀠 16 􀁓 􀀎 48 􀁓  \n􀀠 (64􀁓 )cm 2  \n􀂄 (c) Calculate the volume of the cylinder  \nV  \nV  \nV  \n􀀠 􀁓r 2 h  \n􀀠 􀁓 (4)2 (6)  \n􀀠 (96􀁓 )cm  \n3  \n8  \nEXERCISE  \nCalculate the surface area and volume of a cylinder in each of the following cases:  \n(a) the cylinder is closed and the dimensions are: radius = 5 cm and height = 3 cm.  \n(b) the cylinder is closed and the diameter = 12 cm and the height = 7 cm.  \n(c) the cylinder is open and the dimensions are:  \nradius = 15 cm and height = 8 mm.  \n(d) the cylinder is open and the diameter = 4 cm and the height = cm.","cbCaitPLCwAlls8g","https://ap.wps.com/l/cbCaitPLCwAlls8g","pdf",375834,"English","# RECAP: MEASUREMENT CONCEPTS\n## Building a 3-D Space\n## PRISMS\n### Total Surface Area and Volume\n### Surface Area for Closed vs Open Prisms\n## CYLINDERS\n### Total Surface Area and Volume\n## EXERCISE","[{\"question\":\"What is the total surface area formula for a closed rectangular prism?\",\"answer\":\"Total surface area is TSA = 2LB + 2LH + 2BH, using length (L), breadth (B), and height (H).\"},{\"question\":\"How does the surface area of a prism change when it is open on top?\",\"answer\":\"An open-top prism is missing the top panel, so the surface area uses LB + 2LH + 2BH (top missing).\"},{\"question\":\"How are the formulas for cylinder volume and surface area expressed using radius and height?\",\"answer\":\"Cylinder volume is V = πr²h, and total surface area is given using πr² and the curved-surface term involving πrh, adjusted for whether the cylinder is closed or open-topped.\"}]","Prisms-Cylinders - Measurement | PDF",23]