[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-267091-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-267091-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","ub-sat-2009-worksheet-23a-circles","UB SAT 2009 Worksheet - 23a - Circles","","SAT 2009 Worksheet #23a focuses on circle fundamentals and common geometric relationships. Problems test conversions between area and circumference using π, angle-to-time proportional reasoning, radius determination from given circumference, and arc-length comparisons. Additional items use diagram-based ratios of circle perimeter to arc length, compute unknown chord or segment lengths from radii and areas, and apply scaling of areas from triangle and circle configurations. It also covers percent-change in diameter and composite areas of multiple tangent circles.",{"@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/ub-sat-2009-worksheet-23a-circles/267091/",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/ub-sat-2009-worksheet-23a-circles/267091.png","ImageObject",300,407,{"name":42,"@type":43},"Rizky","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you find a circle’s circumference when its area is given as 64π?","Question",{"text":63,"@type":64},"Use A = πr² to get r² = 64, so r = 8. Then C = 2πr = 16π, which corresponds to option (B).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"If an arc length is 12π and that is 3/4 of the circumference, what is the shortest distance between the arc endpoints?",{"text":68,"@type":64},"First find the full circumference: 12π ÷ (3/4) = 16π, so the radius satisfies 2πr = 16π, giving r = 8. The endpoints subtend a central angle of 270° (the minor arc), so the shortest distance is the chord for 90°, which gives 8√2 (option D).",{"name":70,"@type":61,"acceptedAnswer":71},"How does the area change when a circle’s diameter increases by 50%?",{"text":72,"@type":64},"Diameter scales by 1.5, and area scales by (1.5)² = 2.25. So the area increases by 125% (option D).","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},267091,1789414711,{"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":30,"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":111},962085564807,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","UB SAT 2009  \nWorksheet \\#23a Circles  \n1. If the area of a circle is 64π , then the circumference of the circle is  \n(A) 8π  \n(B) 16π  \n(C) 32π  \n(D) 64π  \n(E) 128π  \n2. If the minute hand of a clock moves 45 degrees, how many minutes of time have passed?(A) 6  \n(B) 7.5  \n(C) 15  \n(D) 30  \n(E) 36.5  \n3. If the circumference of a circle is 1, what is the radius of the circle?  \n(A)  \n(B)  \n(C)  \n(D)  \n(E)  \n1  \n2π  \n 1  \nπ  \n 1  \n2  \nπ 2  \nπ  \nNote: Figure not drawn to scale.  \nA  \nB x°  \nD  \nC  \n4. In the figure above, the ratio of the circumference of circle B to the length of arc ADC is 8 :1 . What is the value of x?  \n5. In the figure above, if the area of the circle with center O is 100π and CA has a length of 6, what is the length of AB?  \n(A) 2 (B) 3 (C) 4 (D) 5 (E) 6  \nX  \nYO  \n6. In the figure above, O is the center of the circle. If the area of triangle XOY is 25, what is the area of the circle?  \n(A) 25π  \n(B) 25π 2  \n(C) 50π  \n(D) 50π 3  \nA B C D  \n7. Each of the 3 shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is  \n(A) 28π  \n(B) 42π  \n10. If an arc with a length of 12π is 34 of the circumference of a circle, what is the shortest distance between the endpoints of the arc?  \n(A) 4  \n(B) 4 2 (C) 8  \n(D) 8 2  \n(E) 16  \n(C) 84π  \n(D) 96π  \n(E) 168π  \nA B  \n11. The total area of the four equal circles in the figure above is 36π , and the circles are all tangent to one another. What is the diameter of the small circle?  \n(A) 6 2  \n(B) 6 + 2  \n8. In the diagram above, if the circle with center A has an area of 72π , what is the area of the circle with center B?  \n(A) 18π  \n(B) 24π  \n(C) 30π  \n(D) 36π  \n(E) 48π  \n(C) 3 2 − 3  \n(D) 6 2 − 6  \n(E) 6 2 + 6  \n9. If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?  \n(A) 25%  \n(B) 50%  \n(C) 100%  \n(D) 125%  \nUB SAT 2009 Worksheet \\#23a Circles Answers  \n1. B 2. B 3. A  \n4. 45 5. A 6. C  \n7. B 8. A 9. D  \n10. D 11. D","cbCairWd9iutjHxA","https://ap.wps.com/l/cbCairWd9iutjHxA","pdf",108607,"English","# Problems\n## Circle measurements and relationships\n## Arc length, sectors, and composite figures\n# Answers","[{\"question\":\"How do you find a circle’s circumference when its area is given as 64π?\",\"answer\":\"Use A = πr² to get r² = 64, so r = 8. Then C = 2πr = 16π, which corresponds to option (B).\"},{\"question\":\"If an arc length is 12π and that is 3/4 of the circumference, what is the shortest distance between the arc endpoints?\",\"answer\":\"First find the full circumference: 12π ÷ (3/4) = 16π, so the radius satisfies 2πr = 16π, giving r = 8. The endpoints subtend a central angle of 270° (the minor arc), so the shortest distance is the chord for 90°, which gives 8√2 (option D).\"},{\"question\":\"How does the area change when a circle’s diameter increases by 50%?\",\"answer\":\"Diameter scales by 1.5, and area scales by (1.5)² = 2.25. So the area increases by 125% (option D).\"}]","UB SAT 2009 Worksheet - 23a - Circles | PDF"]