[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-401758-105":59,"doc-detail-401758-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","prep-expert-digital-sat-playbook-bonus-chapter-ace-3d-figures","Prep Expert Digital SAT Playbook - Bonus Chapter - Ace 3D Figures","","Ace 3D Figures to strengthen SAT Math performance by mastering core volume concepts for common solids. The chapter focuses on knowing and using reference volume formulas for rectangular prisms, cylinders, spheres, cones, and pyramids without relying on memorization. It also teaches how to compute volumes for unreferenced 3D figures by using face area times height. Finally, it clarifies mass, volume, and density and applies these ideas through example questions and practice problems.",{"@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":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/prep-expert-digital-sat-playbook-bonus-chapter-ace-3d-figures/401758/",{"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/prep-expert-digital-sat-playbook-bonus-chapter-ace-3d-figures/401758.png","ImageObject",300,407,{"name":92,"@type":93},"pop out","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why is memorizing 3D figure volume formulas not the main goal for SAT Math?","Question",{"text":112,"@type":113},"The strategy emphasizes learning to use the formulas proficiently during the test, because the reference sheet provides them. The focus is on efficient application rather than rote memorization.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How should you find the volume of a 3D figure that is not on the SAT Math Reference Sheet?",{"text":117,"@type":113},"Compute the area of one face of the figure and multiply that area by the height of the figure.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the difference between mass, volume, and density on SAT Math problems?",{"text":121,"@type":113},"Mass is the amount of the 3D figure (treated like weight for SAT purposes), volume is the space the figure occupies, and density relates mass to volume (mass per unit of space).","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},401758,1791410808,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"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":144,"preview_page_count":4},962090760408,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Prep Expert Math Strategy \\#21:  \nAce 3D Figures  \nPREP EXPERT STRATEGY + EXAMPLE  \nAce 3D Figures  \nTo perform well on SAT Math, you must Ace 3D Figures. Below are the most important concepts to master this topic for the SAT.  \nKey Concepts  \nKey Concept \\#1: Reference Volume Formulas for 3D Figures  \nFamiliarize yourself with the volume formulas for common 3D figures that will be provided on test day on the SAT Math Reference Sheet. Know how to calculate the volume of rectangular prisms, cylinders, spheres, cones, and pyramids.  \nExpert Strategy  \n(1) The goal is not memorization.  \n(2) Instead, learn to use these formulas proficiently to solve volume problems during the test.  \nExpert Example  \nQuestion: What is the volume of a cone with a circle base in which the radius is 3 and the height is 5 ?  \nAnswer:  \n􀕄 = ~~ ~~13~~ ~~π􀕚2ℎ  \n􀕄 = ~~ ~~13~~ ~~ π (3)2 (5)  \n􀕄 = ~~ 1~~3~~ ~~ (45)π  \n􀕄 = 15π  \nKey Concept \\#2: Calculating Volume for Unreferenced 3D Figures  \nYou must also be able to calculate the volume of 3D figures for which the formulas are not directly provided on the SAT Math Reference Sheet on test day.  \nExpert Strategy  \n(1) The SAT may ask you to find the volume of a 3D figure that is not one of the five figures in the SAT Math Reference Sheet.  \n(2) In this case, calculate the area of one face of the figure and multiply it by the height of the figure.  \nExpert Example  \nQuestion:  \nWhat is the volume of the hexagonal prism above, if the area of the hexagonal face is 20 square inches and the height is 5 inches?  \nAnswer:  \n􀕄􀕗􀕔􀕝􀕕􀕍 = 􀕉􀕚􀕍􀕉 􀕗􀕎 􀕊􀕉􀕛􀕍 × ℎ􀕍􀕑􀕏ℎ􀕜  \n􀕄􀕗􀕔􀕝􀕕􀕍 = (20 􀕑􀕖􀕋ℎ􀕍􀕛 2) × (5 􀕑􀕖􀕋ℎ􀕍􀕛 )  \n3  \n􀕄􀕗􀕔􀕝􀕕􀕍 = 100 􀕑􀕖􀕋ℎ􀕍􀕛  \nKey Concept \\#3: Mass, Volume, and Density  \nUnderstanding the differences between mass, volume, and density is essential for SAT Math. You must apply these concepts to problem-solving scenarios that involve physical properties.  \nExpert Strategy  \n(1) Mass is the amount of a 3D figure (for SAT purposes, you can think of mass as weight) .  \n(2) Volume is the amount of space that a 3D figure takes up.  \n(3) Density is ~~ ~~􀕞􀕕􀕗􀕔􀕉􀕝􀕛􀕛􀕕􀕍~~ ~~ (weight per amount of space) .  \nExpert Example  \nQuestion:  \nQuestion 1 : What has a greater volume—a standard-sized helium balloon or an iPhone? Question 2 : What has greater mass—a standard-sized helium balloon or an iPhone? Question 3 : What has greater density—a standard-sized helium balloon or an iPhone?  \nAnswer:  \nAnswer 1  : A standard-sized helium balloon  \nAnswer 2  : An iPhone  \nAnswer 3  : An iPhone  \nAce 3D Figures to maximize your SAT Math score.  \nPREP EXPERT PRACTICE  \nTry applying this Prep Expert Strategy yourself to the following SAT practice questions:  \nA cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume, in cubic centimeters, of the cone?  \nA) 12π  \nB) 36π  \nC) 120π  \nD) 360π  \nA cube has an edge length of 60 centimeters. A solid sphere with a radius of 30 centimeters is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic centimeter, what is the volume of the space in the cube not taken up by the sphere?  \nA) 102, 903  \nB) 113, 097  \nC) 134, 041  \nD) 270, 000  \nThe answers to these SAT practice problems can be found in the back of this book.  \nPREP EXPERT REVIEW  \n\n| KEY TAKEAWAYS |\n| --- |\n| ● Prep Expert Math Strategy \\#20—Ace 3D Figures: This section covered key concepts for mastering 3D figures on SAT Math.\u003Cbr>● Reference Volume Formulas: Familiarize yourself with the volume formulas for standard 3D shapes such as prisms, cylinders, spheres, cones, and pyramids. Focus on using these formulas efficiently, not necessarily memorizing them since they are given to you on the SAT Math Reference Sheet.\u003Cbr>● Unreferenced 3D figure volumes: Be prepared to calculate the volumes of 3D figures that are not listed on the SAT Math Reference Sheet. For such figures, find the area of one face and multiply that area by the height of the figure.\u003Cbr>● Mass, volume, and d","cbCaicLXazHJz5FS","https://ap.wps.com/l/cbCaicLXazHJz5FS","pdf",947703,"English","# Key Concepts\n## Reference Volume Formulas for 3D Figures\n## Calculating Volume for Unreferenced 3D Figures\n## Mass, Volume, and Density\n# Prep Expert Practice\n# Prep Expert Review","[{\"question\":\"Why is memorizing 3D figure volume formulas not the main goal for SAT Math?\",\"answer\":\"The strategy emphasizes learning to use the formulas proficiently during the test, because the reference sheet provides them. The focus is on efficient application rather than rote memorization.\"},{\"question\":\"How should you find the volume of a 3D figure that is not on the SAT Math Reference Sheet?\",\"answer\":\"Compute the area of one face of the figure and multiply that area by the height of the figure.\"},{\"question\":\"What is the difference between mass, volume, and density on SAT Math problems?\",\"answer\":\"Mass is the amount of the 3D figure (treated like weight for SAT purposes), volume is the space the figure occupies, and density relates mass to volume (mass per unit of space).\"}]","Prep Expert Digital SAT Playbook - Bonus Chapter - Ace 3D Figures | PDF",1790523680,18]