[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297470-105":59,"doc-detail-297470-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","surface-areas-and-volumes-chapter-common-mistakes-how-to-avoid","Surface Areas and Volumes - Chapter - Common mistakes & How to avoid","","Surface Areas and Volumes chapter focuses on recurring errors made when solving geometry problems involving combinations of solids such as cones, cylinders, hemispheres, and frustums. It emphasizes correct interpretation of the question (curved surface area vs total surface area, surface area vs volume), proper identification of what must be calculated, and accurate formula usage. Guidance includes drawing labeled figures, tracking visible surfaces, converting units consistently, handling π correctly, and distinguishing volume conservation when solids or water are transferred.",{"@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/surface-areas-and-volumes-chapter-common-mistakes-how-to-avoid/297470/",{"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-areas-and-volumes-chapter-common-mistakes-how-to-avoid/297470.png","ImageObject",300,407,{"name":92,"@type":93},"Pentious","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How can students avoid misinterpreting whether to calculate curved surface area or total surface area?","Question",{"text":113,"@type":114},"Read the question carefully and identify what is asked. Use curved surface area only when that surface is relevant (e.g., cloth/painting for the curved part) and total surface area only when the entire outer surface is required.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Why must units be converted into the same measurement system before calculations?",{"text":118,"@type":114},"Using mixed units leads to incorrect results. Convert all dimensions (e.g., radius and height) to a single unit set before substituting into formulas.",{"name":120,"@type":111,"acceptedAnswer":121},"In water-transfer or material-transfer problems, what stays the same?",{"text":122,"@type":114},"The volume of the material remains the same across the transformation, not the surface areas or the full dimensions of the container. 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Find the | i) Students generally get confused whether the surface area of the big solid is equal to the SA of the smaller | i) When a solid is melted and converted to another, volume of both the solids remains the same, assuming there is no |\n\n| number of smaller solids formed\u003Cbr>-A vessel whose dimensions are given is full of water. The water is emptied into another vessel of different shape with radius given. Find the height to which the water rises in the other vessel. | ones or it’s the volume that is equal.\u003Cbr>ii) Error in considering the surface areas orthe volumes of the two vessels equal\u003Cbr>ii) What should be\u003Cbr>taken as the value of π\u003Cbr>iii) calculation errors | wastage in the conversions. i.e remember\u003Cbr>Volume before = volume after conversion\u003Cbr>We cant predict whether The surface area of the two solids are equal or not\u003Cbr>(ii) Similarly when material is transferred from one solid to another, then also the volume of material in both the solids remains the same.\u003Cbr>i.e the volume of water, which is equal to the volume of the first vessel partially fills the second vessel. Hence, the volume of the first vessel is not equal to the volume of the 2nd vessel.\u003Cbr>For example:\u003Cbr>A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises in the cylindrical vessel.\u003Cbr>Here, Volume of cone = Volume of water = Volume of water in the cylinder ≠ Volume of the cylinder (iii) Value of π if not specified can be taken as 22/7 if radius or height are multiples of 7. Also see if you can cancel out π when equating the volumes.\u003Cbr>(iv) Be careful while calculating look for |\n| --- | --- | --- |\n\n|  |  | simplifying ","cbCaifWjX7AJn1KP","https://ap.wps.com/l/cbCaifWjX7AJn1KP","pdf",359066,"English","# Types of questions\n## Common mistakes and points to be emphasized\n## Unit handling and formula reminders\n## Volume conservation in transformations\n## Frustum of a cone: metal and cost","[{\"question\":\"How can students avoid misinterpreting whether to calculate curved surface area or total surface area?\",\"answer\":\"Read the question carefully and identify what is asked. Use curved surface area only when that surface is relevant (e.g., cloth/painting for the curved part) and total surface area only when the entire outer surface is required.\"},{\"question\":\"Why must units be converted into the same measurement system before calculations?\",\"answer\":\"Using mixed units leads to incorrect results. Convert all dimensions (e.g., radius and height) to a single unit set before substituting into formulas.\"},{\"question\":\"In water-transfer or material-transfer problems, what stays the same?\",\"answer\":\"The volume of the material remains the same across the transformation, not the surface areas or the full dimensions of the container. Match volumes before and after to find the required height or dimensions.\"}]","Surface Areas and Volumes - Chapter - Common mistakes & How to avoid | PDF",1789744822]