[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297345-105":59,"doc-detail-297345-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","automotive-technology-t-chart-surface-area","Automotive Technology T-Chart - Surface Area","","Automotive Technology T-Chart material focused on calculating surface area for solid shapes used in engine and technical applications, especially pistons and cylindrical components. Provides step-by-step formulas and procedures for cylinders, cones, rectangular prisms, spheres, pyramids, and an annulus for brake-related geometry, including examples with radius, diameter, and height. Includes instructor guidance on linking geometry to CTE tasks and highlights common student mistakes such as using incorrect formulas or omitting unnecessary surfaces. Ends with practice problems covering rotors, wheel cylinder seals, traffic-cone pyramids, and generic comparison scenarios.",{"@graph":69,"@context":122},[70,84,105],{"@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":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/automotive-technology-t-chart-surface-area/297345/",{"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/automotive-technology-t-chart-surface-area/297345.png","ImageObject",300,407,{"name":92,"@type":93},"supergirl","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the surface area of a cylinder in this material?","Question",{"text":112,"@type":113},"Use SA = 2πr2 + 2πrh, where r is the radius and h is the height (or pipe/tubing length for technical use).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why does a brake rotor use an annulus surface area approach and what does “2 sides” mean?",{"text":117,"@type":113},"The material gives annulus SA based on the difference between outer and inner radii/diameters. It also reminds that a brake rotor has two sides, so the needed surface area accounts for both braking surfaces.",{"name":119,"@type":110,"acceptedAnswer":120},"What common mistakes do students make when solving surface area problems?",{"text":121,"@type":113},"Students may use the wrong formula for the object type, and they may fail to remove unnecessary surface areas from the calculation when the problem only involves part of the solid.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},297345,1790437716,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52},962088121634,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Calculate surface area of a piston  \n=  \nApply geometric concepts to model and solve real world problems  \nProgram Task: Diagnose engine mechanical problems PA Core Standard: CC 2 3 HS A 14  \n,  \nperform precision measurements.  \nProgram Associated Vocabulary:  \nAREA, DISPLACEMENT, COVERAGE, FRICTION SURFACE, DIAMETER  \nProgram Formulas and Procedures:  \nFormula to find Surface Area: Cylinder: SA = 2πr2 + 2πrh r = radius, h = height  \ndiameter = 4”  \nh = 5”  \nExample: What is the surface area of this piston? Radius is ½ of diameter = 0.5 x 4 = 2”  \nh(height) = 5”  \nCylinder SA = 2πr2 + 2πrh  \nSA = 2×π×22 + 2×π×2×5  \nSA = 8π + 20π  \nSA = 28×π  \nSA ≈ 87.92 [sq. in](sq. in).  \n. . . . .  \nDescription: Apply geometric concepts to model and solve real world problems.  \nMath Associated Vocabulary:  \nAREA, CROSS SECTION, LENGTH, WIDTH, ROUND, BASE, HEIGHT, RADIUS, RECTANGULAR PRISM  \nFormulas and Procedures: Surface Area:  \nCylinder:  \nSA = 2 π r2 + 2 π r h  \nCone:  \nSA = π r2 + πr (r2+h2)  \nRectangular Prism:  \nSA = 2lw + 2wh+ 2hl  \nSphere:  \nSA = 4 π r2  \nPyramid:  \nSA = (area of the base) + ½ l(perimeter of base) h = height, b= base, l= slant length  \n60”  \nExample: Find the surface area of the cylinder above. r = ½ • 38” = 19” h = 60”  \nCylinder SA = 2πr2 + 2πrh  \nSA = 2π(19)2 + 2π(19)(60)  \nSA = 722π + 2,280π  \nSA = 3,002π  \nSA ≈ 9,426.28 in2  \nInstructor’s Script – Comparing and Contrasting  \nSurface Area is the total area of all surfaces of a solid object. Unlike lateral area, it includes the area of the bases ofthe figure. The surface area formulas used in technical trades are the same as in mathematics:  \nThe formulas correspond to the areas of the individual surfaces ofthe objects:  \nCylinder SA = 2πr2 + 2πrh (r = radius, h = height/length)  \nArea of top & bottom (2 circles) + Area of sides  \nCone SA = πr2 + πrl(r = radius, l = slant height)  \nArea of bottom (circle) + Area of side  \nCube SA = 6e2 (e = length of single edge of cube)  \nArea of 6 sides (6 squares)  \nPyramid SA = B + ½ lp (p = perimeter of base, l = slant height)  \nArea of base + Area of sides  \nOne additional surface area formula useful in some automotive applications (e.g., brakes) is the annulus:  \nAnnulus SA = π(r22 – r12) OR (using diameter): SA = .7854 (d22 – d12)  \n**Remember when computing surface area of a brake rotor that it has 2 sides!  \nWhen using these surface area formulas for technical applications, the student must identify which parts of the formulas to use, as many applications will not be concerned with ALL surfaces ofan object.  \nr2 r1  \nFor example, cylinders include a top and bottom (2πrh), but if you are calculating a hemi cylinder, you will want to remove the top from the math formula and replace it with a specialized formula for the cap.  \nCommon Mistakes Made By Students  \nUsing incorrect formula: Students may use an incorrect formula to solve a problem. To rectify these errors have the students correctly identify the type of object they are dealing with and use the appropriate formula. Frequently two formulas may be needed for complex problems.  \nNot “removing” unnecessary surface areas from calculations: Depending on the problem, not all surface areas included in formula may be needed. Identify the areas that are required for the calculation and remove from formula as needed.  \nCTE Instructor’s Extended Discussion  \nTechnical tasks are usually not presented using this model. Therefore, it is important that technical instructors demonstrate to students how these math concepts link to and are relevant in their technical training and that the math is presented in a way which shows a relationship to the math CTE students use in their academic school settings.  \nMany shapes addressed in geometry books can be found in the automotive technology industry; cylindrical shapes being the most frequently utilized. This T-Chart focuses on determining the surface area of pistons. In addition to engine cylinders and pistons, other cylindrical part","cbCaisGm2YNbHXjF","https://ap.wps.com/l/cbCaisGm2YNbHXjF","pdf",311004,"English","# Surface Area of a Piston (Cylinder Model)\n## Core Definitions and Key Vocabulary\n## Surface Area Formulas for Common Solids\n## Brake Rotor and Annulus Applications\n## Instructor Guidance: Comparing and Contrasting\n## Common Student Mistakes\n## Extended Discussion Linking to Automotive Technology\n## Practice Problems","[{\"question\":\"How do you find the surface area of a cylinder in this material?\",\"answer\":\"Use SA = 2πr2 + 2πrh, where r is the radius and h is the height (or pipe/tubing length for technical use).\"},{\"question\":\"Why does a brake rotor use an annulus surface area approach and what does “2 sides” mean?\",\"answer\":\"The material gives annulus SA based on the difference between outer and inner radii/diameters. It also reminds that a brake rotor has two sides, so the needed surface area accounts for both braking surfaces.\"},{\"question\":\"What common mistakes do students make when solving surface area problems?\",\"answer\":\"Students may use the wrong formula for the object type, and they may fail to remove unnecessary surface areas from the calculation when the problem only involves part of the solid.\"}]","Automotive Technology T-Chart - Surface Area | PDF",1789744032]