[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-297347-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-297347-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","cone-tastic-volume-of-a-cone-lesson-2","Cone-tastic! - Volume of a Cone - Lesson 2","","Grade 8 lesson materials guide students to calculate and compare the volume of cones. Learners sketch cones, identify radius, diameter, height, and use volume formulas related to cylinders and pyramids to derive V = Bh and V = πr2h. Students solve problems with given dimensions, including using slant height to find missing values, and compare conical versus cylindrical popcorn containers to connect matching base area and height.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/cone-tastic-volume-of-a-cone-lesson-2/297347/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/cone-tastic-volume-of-a-cone-lesson-2/297347.png","ImageObject",300,407,{"name":42,"@type":43},"eBook King","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",15,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What key measurements do students identify for a cone?","Question",{"text":63,"@type":64},"Students identify the radius, diameter, and height of the cone. They use these measurements to work with volume formulas.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do students derive the volume formula for a cone?",{"text":68,"@type":64},"Students relate cones to pyramids and cylinders, leading to the general form V = Bh and the cone-specific form V = πr2h.",{"name":70,"@type":61,"acceptedAnswer":71},"How is slant height used in cone volume problems?",{"text":72,"@type":64},"Students use the Pythagorean Theorem to determine the height of a cone when given the radius and slant height, then apply the volume formula.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},297347,1789744038,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},962088006270,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Cone-tastic!  2   \nVolume of a Cone  \nMATERIALS  \nNone  \nLesson Overview  \nStudents learn how to calculate the volume of a cone and solve problems involving cones. They sketch a cone and answer questions relevant to their sketches. Students use the formula for the volume of a cylinder and the volume of a pyramid to write the formula for the volume of a cone. They solve problems when given different dimensions of a cone, including the slant height. Students learn how to determine a missing dimension using the formula for the volume of a cone. They also determine the volume of cylindrical and conical popcorn containers and the relationship between them.  \nGrade 8  \nExpressions, Equations, and Relationships  \n(6) The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:  \n(B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.  \n(7) The student applies mathematical process standards to use geometry to solve problems. The student is expected to:  \n(A) solve problems involving the volume of cylinders, cones, and spheres.  \n(C) use the Pythagorean Theorem and its converse to solve problems.  \nELPS  \n1.A, 1. D, 1. E, 1.G, 2.C, 2. D, 2.G, 2. H, 2. I, 3.A, 3. B, 3.C, 3. D, 3. F, 4.A, 4. B, 4.C, 4.G, 4. K, 5. E  \nEssential Ideas  \n• A cone is a three-dimensional object with a circular base and one vertex.  \n• The formula for the volume of a cone can be written two different ways: as V =  Bh, where V is the volume, B is the area of the base, and h is the height, and as V =  πr2h, where V is the volume, r is the length of the radius of the base, and h is the height.  \n• The Pythagorean Theorem is used to determine the height of a cone, when given the length of the radius and the slant height.  \nLESSON 2: Cone-tastic! • 1  \nLesson Structure and Pacing: 1 Session  \nEngage  \nGetting Started: All About Cones  \nStudents learn the formal terminology for cones. They sketch an example of a cone and answer questions relevant to their sketches. Cones are distinguished by the length of the radius of their bases and their height. Students identify the radius, the diameter, and the height of the cones.  \nDevelop  \nActivity 2.1: Volume Formula for a Cone  \nStudents notice that as the number of sides on the bases of pyramids increases, the shape of the pyramid approaches the shape of a cone. Students develop formulas for the volume of a cone by relating it to pyramids and cylinders. The formula for the volume of a cone can be expressed in a general form, V =  Bh, and in a cone-specific form, V =  πr2h.  \nActivity 2.2: Problem Solving with Cones  \nStudents solve problems involving the volume of cones. They determine which of a set of three cones has the largest volume. Next, they analyze solutions to a problem in which the slant height, rather than the actual height, of the cone is given. Students then calculate the volume of cones given different information, and they determine dimensions of cones given their volumes.  \nActivity 2.3: Cone Vs. Cylinder  \nA cylindrical and conical container are shown, each holding the same amount of popcorn. Students are given the length of the radius of the circular base of the cylinder and the height of the cylinder. Using this information, they determine the volume and surface area of the open cylindrical container and the length of the radius of the conical container. Students then compare the volumes of a conical container and open cylindrical container with the same height and radius. They will conclude that the volume of a conical container is  the volume of the open cylindrical container.  \nDemonstrate  \nTalk the Talk: Show What You Know  \nStudents complete a formative assessment to demonstrate their learning from the lesson.  \n2 • SUMMER LEARNING TOPIC 4: Volume and Surface Area  \nGetting Started: All About Cone","cbCaisJiSadM2sQb","https://ap.wps.com/l/cbCaisJiSadM2sQb","pdf",684776,17,"English","# Lesson Overview\n## Engage: Getting Started: All About Cones\n## Develop\n### Activity 2.1: Volume Formula for a Cone\n### Activity 2.2: Problem Solving with Cones\n### Activity 2.3: Cone Vs. Cylinder\n## Demonstrate: Talk the Talk\n## Summary","[{\"question\":\"What key measurements do students identify for a cone?\",\"answer\":\"Students identify the radius, diameter, and height of the cone. They use these measurements to work with volume formulas.\"},{\"question\":\"How do students derive the volume formula for a cone?\",\"answer\":\"Students relate cones to pyramids and cylinders, leading to the general form V = Bh and the cone-specific form V = πr2h.\"},{\"question\":\"How is slant height used in cone volume problems?\",\"answer\":\"Students use the Pythagorean Theorem to determine the height of a cone when given the radius and slant height, then apply the volume formula.\"}]","Cone-tastic! - Volume of a Cone - Lesson 2 | PDF",43]