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Includes a sample problem for finding the length of an arc and the area of a shaded sector, followed by a structured set of practice problems where students fill in θ, radius values, and computed results. Additional homework problems address circle length and area using π, plus geometry practice that connects to perpendicular lines.",{"@graph":69,"@context":114},[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/arc-length-sector-area-practice-problems/357057/",{"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/arc-length-sector-area-practice-problems/357057.png","ImageObject",300,407,{"name":92,"@type":93},"Himbo","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"What should students do when a problem says to leave the answer in terms of pi?","Question",{"text":112,"@type":113},"Compute the result symbolically using π rather than converting to a decimal.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},357057,1790719179,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":131,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":67,"update_tm":135,"read_time":46,"preview_page_count":4},687197100911,"https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697","Name:   Date:    \n\n| | \u003Cbr>ARC LENGTH | SECTOR AREA |\n| --- | --- | --- |\n| Formula | l = θ~~ ~~r8~~ ~~π | θ 2\u003Cbr>A =  2  r (in radians), or A = ~~ ~~3θ60 r 2 (in degrees) |\n| When to Use | When finding the length of an arc (a portion of the circumference) given the angle ( θ ) and the radius (r) . | When finding the area sector (or portion of) a circle . |\n| Diagram | | |\n\nSAMPLE PROBLEM: Find the length of arc AB and the area of the shaded region  \nGIVE AN EXACT ANSWER AND IN TERMS OF π .  \n| ARC LENGTH | SECTOR AREA |\n| --- | --- |\n\nθ =  \nr =  \nr 2 =  \n| l = θ × 1π80 × r | θ 2\u003Cbr>A =  2  r (in radians), or A = ~~ ~~3θ60 r 2 (in degrees) |\n| --- | --- |\n\nARC LENGTH SECTOR AREA  \nPRACTICE PROBLEMS: Find the ARC LENGTH and SECTOR AREA of each of the following:  \n\n| PROBLEM | ARC LENGTH | SECTOR AREA |\n| --- | --- | --- |\n| 1.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n| 2.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n\n\n| PROBLEM | ARC LENGTH | SECTOR AREA |\n| --- | --- | --- |\n| 3.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n| 4.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n| 5.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n\n\n| PROBLEM | ARC LENGTH | SECTOR AREA |\n| --- | --- | --- |\n| 6.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n| 7.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n| 8.)\u003Cbr>\u003Cbr>θ = r = r 2 = | In terms of π :\u003Cbr>Exact Answer: | In terms of π :\u003Cbr>Exact Answer: |\n\nNAME:    \nIf you do not try, then you can never learn!  \n\n| \u003Cbr>ARC LENGTH SECTOR AREA CIRCUMFERENCE & AREA |  |  |\n| --- | --- | --- |\n| l = θ ×  π  × r | θ 2\u003Cbr>A =  2  r (in radians), or | C = πd |\n| 180 | θ 2\u003Cbr>A =  360 r (in degrees) | A = πr2 |\n\n1.) What is the length of the line connecting the points (-4,2) and (10, -2)?  \nROUND ANSWER TO THE NEAREST WHOLE NUMBER.  \nMy Answer:    \n2.) What is the circumference of a circle with a radius of 12 feet?  \nMy Answer:    \n3.) What is the area of a circle with a diameter of 21 yards?  \nMy Answer:    \n4.) What is the length of arc AB in the circle below (leave answer in terms of pi)?  \nMy Answer:    \n5.) Carlos operates a pizzeria in Chicago. If the diameter of a large pie at his restaurant is 24 inches, what would be the area of one slice (if every pizza is cut into 8 equal slices)?  \nROUND ANSWER TO THE NEAREST TENTH OF AN INCH.  \nMy Answer:  \n_________  \nNAME:    \nGEOMETRY HOMEWORK  \nDATE:    \nNO WORK = NO CREDIT!!!  \n\n| 1.) What is the apparent slope of the given\u003Cbr>\u003Cbr>My Answer:   |  | 2.) Approximately how many feet of rope would be needed to make a circle with a radius of 10 feet (use π = 3.14 if you do not have a graphing calculator)?\u003Cbr>My Answer:   |  |\n| --- | --- | --- | --- |\n| 3.) What is the area of the given circle (use π = 3.14 if you do not have a graphing calculator)? |  | 4.) What is the arc length of PQ (give your answer in terms of pi) . |  |\n| | My Answer:   | | My Answer:   |\n| 5.) What is the area of the shaded region in the circle below (leave you answer in terms of pi) . |  |  |  |\n| |  | My Answer:   |  |\n\nNAME:   DATE:    \nTopic Review: Perpendicular Lines  \nModel Problems:  \n\n| Example \\#1:\u003Cbr>Which of the following lines would be perpendicular to the line y = 67 x + 2 ?\u003Cbr>a) y = − ~~ ~~67 x + 3 b) y = 67 x − 5\u003Cbr>c) y = − ~~ ~~76 x − 5 d) y = 76 x + 2 | Example \\#2:\u003Cbr>\u003Cbr>Through the given point, construct a line that is perpendicular to the given line. |\n| --- | --- |\n\nPRACTICE PROBLEMS:  \n1.) Write the negative reciprocal of each of the following slopes:  \n\n| 2 3 | 4\u003Cbr>−\u003Cbr>5 | 6 8 | −3 |  1\u003Cbr>−\u003Cbr>4 |\n| --- | --- | --- | --- | --- |\n| 5 | 1\u003Cbr>−\u003Cbr>3 | 5 3 | 12\u003Cbr>−\u003Cbr>13 | 1 |\n\n2.) Match each line with the letter of the line ","cbCaifKM25xp6oht","https://ap.wps.com/l/cbCaifKM25xp6oht","pdf",1524331,"English","# Sample Problem\n## Arc Length and Sector Area\n# Practice Problems\n## Fill in θ and radius values\n# Additional Circle and Arc Problems\n## Exact answers in terms of π\n# Topic Review: Perpendicular Lines\n## Negative reciprocal of slopes\n## Construct perpendicular lines","[{\"question\":\"What should students do when a problem says to leave the answer in terms of pi?\",\"answer\":\"Compute the result symbolically using π rather than converting to a decimal.\"}]","Arc Length - Sector Area - Practice Problems | PDF",1790128764]