[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-497462-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-497462-en":130},{"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","volume-of-cylinders-cones-and-spheres-practice","Volume of Cylinders, Cones, and Spheres - Practice","","Volume measures how much space a solid fills, using π-based formulas for cylinders, cones, and spheres. The quick review explains V = πr2h for cylinders, V = (1/3)πr2h for cones, and V = (4/3)πr3 for spheres, emphasizing radius use and leaving answers in terms of π unless π ≈ 3.14 is requested. Practice problems cover multiple cylinders, cones, and spheres plus real-world word problems about water tanks, ice cream cones, basketballs, and cans, with answer keys and step-by-step solutions.",{"@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/volume-of-cylinders-cones-and-spheres-practice/497462/",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/volume-of-cylinders-cones-and-spheres-practice/497462.png","ImageObject",300,407,{"name":42,"@type":43},"awa","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02","2026-10-02",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What formulas are used to find the volume of a cylinder, cone, and sphere?","Question",{"text":63,"@type":64},"A cylinder uses V = πr2h. A cone uses V = (1/3)πr2h. A sphere uses V = (4/3)πr3.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"When should answers be left in terms of π versus using π ≈ 3.14?",{"text":68,"@type":64},"Leave answers in terms of π unless a problem specifically instructs using π ≈ 3.14. When instructed, compute with 3.14 and round as directed.",{"name":70,"@type":61,"acceptedAnswer":71},"Why is the radius used instead of the diameter in these volume problems?",{"text":72,"@type":64},"The problems require radius because the formulas use r. The radius is half the diameter, so using r ensures the calculations match the given expressions.","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},497462,1791670483,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":110,"preview_page_count":4},3985747858093,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Practice • Progress • Succeed | Colorado CMAS Grade 8 Math [8.G.C, 8.G.C.9]  \n  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nVolume of Cylinders, Cones, and Spheres  \n\n| Name:   | D | ate:   | S | core:   / 24 |\n| --- | --- | --- | --- | --- |\n\nQuick Review  \nVolume measures how much space a solid fills. For a cylinder, V = πr2 h—the circle area πr2 times the height. A cone with the same base and height holds exactly one third as much: V = ~~1~~3πr2 h. A sphere uses V = ~~4~~3πr3 . Always use the radius (half the diameter), and keep your answer in terms of π unless you’re told to use π ≈ 3.14. Volume is measured in cubic units.  \n⋄ Example: Find the volume of a cylinder with radius 3 cm and height 10 cm. Leave your answer in terms of π .⇒ The formula for a cylinder is V = πr2 h. Plug in r = 3 and h = 10: first square the radius, 32 = 9 . Then multiply by the height: 9 × 10 = 90 . So the volume is 90π cubic centimeters. Keeping the π symbol gives an exact answer.  \nAnswer: V = 90π cm3  \nPRACTICE  \nFind each volume. Leave answers in terms of π unless noted.  \n1. Cylinder: r = 5, h = 8    \n2. Cylinder: r = 2, h = 7    \n3. Cylinder: r = 4, h = 6    \n4. Cylinder: r = 10, h = 10    \n5. Cylinder: r = 6, h = 5    \n6. Cylinder: d = 6, h = 9    \n7. Cone: r = 3, h = 9    \n8. Cone: r = 6, h = 10    \n9. Cone: r = 5, h = 12    \n10. Cone: r = 2, h = 6    \n11. Cone: r = 9, h = 4    \n12. Cone: r = 3, h = 7    \n13. Sphere: r = 3    \n14. Sphere: r = 6    \n15. Sphere: r = 9    \n16. Sphere: r = 1    \n17. Sphere: d = 12    \n18. Cylinder: r = 1, h = 9    \n19. Cone: r = 6, h = 5 , use π ≈ 3.14    \n20. Cylinder: r = 2, h = 10 , use π ≈ 3.14    \n♦ Word Problems  \n21. A water tank is a cylinder with radius 4 ft and height 6 ft. Find its volume in terms of π .    \n22. An ice cream cone has radius 3 cm and height 9 cm. How much ice cream fills it exactly? Leave your answer in terms of π .  \n23. A basketball is a sphere with radius 6 inches. Find its volume in terms of π .    \n24. A cylindrical can has radius 2 cm and height 10 cm. Using π ≈ 3. 14, find its volume to the nearest tenth.    \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nPractice • Progress • Succeed | Colorado CMAS Grade 8 Math [8.G.C, 8.G.C.9]  \n  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1. 200π 13. 36π  \n2. 28π 14. 288π  \n3. 96π 15. 972π  \n4. 1000π 16.  ~~4~~3π   \n5. 180π 17. 288π  \n6. 81π 18. 9π  \n7. 27π 19. 188.4  \n8. 120π 20. 125.6  \n9. 100π 21. 96π ft3  \n10. 8π 22.  27π cm3   \n11. 108π 23.  288π in3   \n12. 21π 24.  125.6 cm3   \nStep-by-Step Explanations  \n1. V = πr2 h = π(25)(8) = 200π .  \n2. V = π(4)(7) = 28π .  \n3. V = π(16)(6) = 96π .  \n4. V = π(100)(10) = 1000π .  \n5. V = π(36)(5) = 180π .  \n6. Radius is 3, so V = π(9)(9) = 81π .  \n7. V = ~~1~~3πr2 h = ~~1~~3π(9)(9) = 27π .  \n8. V = ~~1~~3π(36)(10) = 120π .  \n9. V = ~~1~~3π(25)(12) = 100π .  \n10. V = ~~1~~3π(4)(6) = ","cbCaiv9J9qqPRVBB","https://ap.wps.com/l/cbCaiv9J9qqPRVBB","pdf",405552,"English","# Quick Review\n## Practice\n## Word Problems\n## Answer Keys\n## Step-by-Step Explanations","[{\"question\":\"What formulas are used to find the volume of a cylinder, cone, and sphere?\",\"answer\":\"A cylinder uses V = πr2h. A cone uses V = (1/3)πr2h. A sphere uses V = (4/3)πr3.\"},{\"question\":\"When should answers be left in terms of π versus using π ≈ 3.14?\",\"answer\":\"Leave answers in terms of π unless a problem specifically instructs using π ≈ 3.14. When instructed, compute with 3.14 and round as directed.\"},{\"question\":\"Why is the radius used instead of the diameter in these volume problems?\",\"answer\":\"The problems require radius because the formulas use r. The radius is half the diameter, so using r ensures the calculations match the given expressions.\"}]","Volume of Cylinders, Cones, and Spheres - Practice | PDF",1790956676]