[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297250-105":59,"doc-detail-297250-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","areas-and-volumes-of-solids-learn-surface-area-and-volume-formulas-for-prisms-cylinders-and-spheres","Areas and Volumes of Solids - Learn surface area and volume formulas for prisms, cylinders, and spheres","","Areas and Volumes of Solids introduces how to calculate volumes of rectangular prisms, cylinders, and spheres, and how to determine surface areas for cylinders and spheres. It explains SI volume units, including conversions that preserve cubic relationships between m3, cm3, mm3, and litres (L = 1 dm3). Worked examples apply length x width x depth for prisms, πDh and πDh + 2(0.7854D2) for cylinders, and 4πr2 and (4/3)πr3 for spheres.",{"@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/areas-and-volumes-of-solids-learn-surface-area-and-volume-formulas-for-prisms-cylinders-and-spheres/297250/",{"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/areas-and-volumes-of-solids-learn-surface-area-and-volume-formulas-for-prisms-cylinders-and-spheres/297250.png","ImageObject",300,407,{"name":92,"@type":93},"Lucas Martin","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",18,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you convert between cubic volume units such as m3 and cm3?","Question",{"text":113,"@type":114},"Use cubic relationships: 1 m3 equals 100 cm x 100 cm x 100 cm, giving 1,000,000 cm3. Linear conversion errors lead to incorrect results (e.g., 0.5 m3 is not 50 cm3).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the formula for the volume of a rectangular prism?",{"text":118,"@type":114},"The volume equals length x width x depth, with all dimensions measured in the same units to give the correct volume unit (e.g., metres for m3, centimetres for cm3).",{"name":120,"@type":111,"acceptedAnswer":121},"How do you calculate the total surface area and volume of a cylinder?",{"text":122,"@type":114},"Total surface area is lateral area plus areas of the two bases: A_T = πDh + 2(0.7854D2). Volume is found from base area times height: V = 0.7854D2h.","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},297250,1789743375,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Areas and Volumes of Solids  \nLearning Outcome  \nWhen you complete this module you will be able to:  \nCalculate the volumes of rectangular objects, cylinders, and spheres and the surface areas of cylinders and spheres.  \nLearning Objectives  \nHere is what you will be able to do when you complete each objective:  \n1. Convert the commonly used units of volume.  \n2. Calculate the volume of a rectangular prism.  \n3. Calculate the surface area and volume of a cylinder.  \n4. Calculate the surface area and volume of a sphere.  \nMATH 6001  \n1  \n2  \nINTRODUCTION  \nFigures having three dimensions such as length, width and thickness are known as solids, and the methods used for finding volume and area of selected solids are discussed in this module.  \nVOLUME  \nVolume is a measure of the three dimensional (height, width, length) capacity of an object. In S.I., the basic unit of volume is the cubic metre, abbreviated m3.  \n1 m3 = 1 m x 1 m x 1 m  \nIn practice, cubic metres are quite large, so to avoid always having to use decimal or fractional quantities of cubic metres, we employ volume units which are derived from the S.I. submultiples ofthe metre. For example:  \n1 cm3 = 1 cm x 1 cm x 1 cm  \n(In past years, a cm3 was also commonly referred to as a c.c. for cubic centimetre) 1 mm3 = 1 mm x 1 mm x 1 mm  \nNote, that in converting from one set of volume units to another, we must maintain the \"cubic\" relationships. For example, if we wish to convert 1 m3 into cm3 we must do the following:  \n1 m3 = 1 m x 1 m x 1 m  \n= 100 cm x 100 cm x 100 cm  \n= 1 000 000 cm3  \n(It is a common error for students to employ the linear relationship and incorrectly conclude that 1 m3 = 100 cm3 !)  \nConvert 0.5 m3 into cm3.  \n1 m3 = 1 m x 1 m x 1 m  \n1 m3 = 100 cm x 100 cm x 100 cm  \n1 m3 = 1 000 000 cm3  \n0.5 m3 = 0.5 x 1 000 000 cm3  \n= 500 000 cm3 (Ans.)(Again, notice that 0.5 m3 ≠ 50 cm3)  \nMATH 6001  \nOne commonly used unit of volume [in S.I. is](in S.I. is) the litre. By definition 1 L = 1 dm3 (dm = decimetre or 0.1 m) . You may wish to verify for yourself that this definition also means that:  \n1 L = 1000 cm3 and 1 m3 = 1000 L  \nVolumes of Rectangular Prisms  \nThe volume of a rectangular prism equals length x width x depth, each dimension being taken in the same units, that is to say, all dimensions must be in centimetres to give volume in centimetres, all in metres to give volume in metres, and so on.  \nExample 1:  \nA rectangular tank is 6 m long and 4 m wide and 2 m deep. What is its capacity in m3?  \nVolume = length x width x depth  \n= 6 x 4 x 2  \n= 48 m3 (Ans.)  \nExample 2:  \nThe base of a 27.3 kL storage tank is 4 m by 4.2 m. To what height must the tank be built?  \nSolution:  \n27.3 kL = 27.3 m3  \nThen divide the volume in m3 by the area of the base in m2 to get the height in m. Height = Volume  \nArea  \n=  27.3   \n4 x 4.2  \n= 1.625 m (Ans.)  \nMATH 6001  \n3  \n4  \nSURFACE AREA OF CYLINDERS  \nIf the shell or lateral surface of a cylinder could be unrolled and spread out as shown in Fig. 1, it would form a rectangle of length equal to the circumference (πD) of the cylinder end and a width equal to the height (h) of the cylinder.  \nThe total surface area of the cylinder is the lateral surface area plus the area of the two ends or bases.  \nLateral surface area = πDh  \nArea of two bases = 2 x (0.7854 D2) Total surface area = πDh + 2 x (0.7854D2)  \nNote: 0.7854 = π/4  \nFigure 1  \nSurface Area  \nExample 3:  \nA cylindrical tank is 5 m in diameter and 22 m long. Find its lateral surface area.  \nSolution:  \nLateral surface area = πDh  \n= 3.1416 x 5 m x 22 m  \n= 345.6 m2 (Ans.)  \nMATH 6001  \nExample 4:  \nCalculate the surface area of a cylindrical fuel tank with flat ends if the tank is 10 m long and 6 m in diameter.  \nSolution:  \nLateral (shell) surface area (AS):  \nAS = πDh  \n= 3.1416 x 6 m x 10 m  \n= 188.5 m²  \nArea of the two ends (AE):  \nAE = 2 x (0 .7854 D2)  \n= 2 x [0.7854 x (6 m)2]  \n= 56.5 m2  \nTotal surface area (AT):  \nAT = AS + AE  \n= 188.5 m2 + 56.5 m2","cbCaioGePLzgvYZY","https://ap.wps.com/l/cbCaioGePLzgvYZY","pdf",143716,14,"English","# Introduction\n# VOLUME\n## Volume units and cubic conversions\n# Volumes of Rectangular Prisms\n# Surface Area of Cylinders\n## Lateral surface area and total surface area\n# Volume of Cylinders\n# Surface Area of Spheres\n# Volume of Spheres","[{\"question\":\"How do you convert between cubic volume units such as m3 and cm3?\",\"answer\":\"Use cubic relationships: 1 m3 equals 100 cm x 100 cm x 100 cm, giving 1,000,000 cm3. Linear conversion errors lead to incorrect results (e.g., 0.5 m3 is not 50 cm3).\"},{\"question\":\"What is the formula for the volume of a rectangular prism?\",\"answer\":\"The volume equals length x width x depth, with all dimensions measured in the same units to give the correct volume unit (e.g., metres for m3, centimetres for cm3).\"},{\"question\":\"How do you calculate the total surface area and volume of a cylinder?\",\"answer\":\"Total surface area is lateral area plus areas of the two bases: A_T = πDh + 2(0.7854D2). Volume is found from base area times height: V = 0.7854D2h.\"}]","Areas and Volumes of Solids - Learn surface area and volume formulas for prisms, cylinders, and spheres | PDF",35]