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Additional problems include 3D volume calculations for cubes and inscribed spheres, cylinder volume relationships, and determining what extra information proves similarity or congruence.",{"@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/hard-geometry-3d-wksht-practice-geometry-and-trigonometry-problems/267039/",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/hard-geometry-3d-wksht-practice-geometry-and-trigonometry-problems/267039.png","ImageObject",300,407,{"name":42,"@type":43},"Seraphina","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",20,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What topics are covered in these SAT math geometry questions?","Question",{"text":63,"@type":64},"The document covers lines, angles, triangles, area and volume, and proofs related to similarity and congruence.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are angle and intersecting-line problems typically approached here?",{"text":68,"@type":64},"They provide specific angle measures or relationships from a figure, then ask for the value of a target angle in degrees.",{"name":70,"@type":61,"acceptedAnswer":71},"What types of 3D volume problems appear in the worksheet?",{"text":72,"@type":64},"It includes calculations such as finding remaining volume in a cube not taken by an inscribed sphere and interpreting radius/height relationships from cylinder volume scaling.","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},267039,1789414159,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"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":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":55,"slug":118},9,"Religion & Spirituality","religion-spirituality",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":55,"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":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144},962075114101,"https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165","Question ID 6d99b141  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 6d99b141  \nIn the figure,  . The measure of angle  is   , and the measure of angle  is   . What is the value of ?  \nQuestion ID e10d8313  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: e10d8313  \nIn the figure shown, points , , , and  lie on line segment , and line segment  intersects line segment  at point  . The measure of  is   , the measure of  is   , the measure of  is   , and the measure of  is   . What is the measure, in degrees, of ?  \nQuestion ID f88f27e5  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: f88f27e5  \nIntersecting lines r, s, and t are shown below.  \nWhat is the value of x ?  \nQuestion ID e5c57163  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Area and volume | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: e5c57163  \nSquare A has side lengths that are  times the side lengths of square B. The area of square A is  times the area of square B. What is the value of ?  \nQuestion ID 947a3cde  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\n ID: 947a3cde   \nIn the figure above,  and  intersect at point P, , and  . What is the measure, in degrees, of  ? (Disregard the degree symbol when gridding your answer.)  \nQuestion ID 9966235e  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Area and volume | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 9966235e  \nA cube has an edge length of  inches. A solid sphere with a radius of  inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?  \nA.   \nB.   \nC.    \nD.    \nQuestion ID a0369739  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: a0369739  \nIn triangle , the measure of angle  is  and  is an altitude of the triangle. The length of  is  and the length of is  greater than the length of  . What is the value of ~~ ~~ ?  \nA. ~~ ~~  \nB. ~~ ~~  \nC. ~~ ~~  \nD. ~~ ~~  \nQuestion ID a07ed090  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Area and volume | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: a07ed090  \nThe figure shown is a right circular cylinder with a radius of  and height of  . A second right circular cylinder (not shown) has a volume that is  times as large as the volume of the cylinder shown. Which of the following could represent the radius , in terms of , and the height , in terms of , of the second cylinder?  \nA.  and   \nB.  and   \nC.  and   \nD.  and   \nQuestion ID f7dbde16  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: f7dbde16  \nIn triangles  and , angles  and  each have measure   , , and  . Which additional piece of information is sufficient to prove that triangle  is similar to triangle ?  \nA.  and   \nB.  and   \nC. The measures of angles  and  are   and   , respectively.  \nD. The measures of angles  and  are   and   , respectively.  \nQuestion ID 901c3215  \n\n| Assessment\u003Cbr>SAT | Test\u003Cbr>Math | Domain\u003Cbr>Geometry and Trigonometry | Skill\u003Cbr>Lines, angles, and triangles | Difficulty\u003Cbr>|\n| --- | --- | --- | --- | --- |\n\nID: 901c3215  \nIn triangles  and , angles  and  each have measure   and angles  and  each have measure   . Which a","cbCaihut9FiB9jcx","https://ap.wps.com/l/cbCaihut9FiB9jcx","pdf",854601,31,"English","# Geometry and Trigonometry Questions\n## Lines, Angles, and Triangles\n## Area and Volume\n## Similarity and Congruence","[{\"question\":\"What topics are covered in these SAT math geometry questions?\",\"answer\":\"The document covers lines, angles, triangles, area and volume, and proofs related to similarity and congruence.\"},{\"question\":\"How are angle and intersecting-line problems typically approached here?\",\"answer\":\"They provide specific angle measures or relationships from a figure, then ask for the value of a target angle in degrees.\"},{\"question\":\"What types of 3D volume problems appear in the worksheet?\",\"answer\":\"It includes calculations such as finding remaining volume in a cube not taken by an inscribed sphere and interpreting radius/height relationships from cylinder volume scaling.\"}]","HARD geometry & 3D WKSHT - Practice Geometry and Trigonometry Problems | PDF",78]