{"id":265,"date":"2017-08-23T04:34:49","date_gmt":"2017-08-23T04:34:49","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/elementary-education\/?page_id=265"},"modified":"2017-09-25T21:20:49","modified_gmt":"2017-09-25T21:20:49","slug":"measuring-circles","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-circles\/","title":{"rendered":"Measuring Circles"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-quadrilaterals\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measurements-involving-three-dimensional-figures\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Measuring Circles<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson you will learn to find the circumference and area of a circle.<\/p>\n<h4>Previously Covered<\/h4>\n<ul>\n<li>Previously, we reviewed formulas to measure triangles and quadrilaterals.<\/li>\n<\/ul>\n<section>\n<h3>About Circles<\/h3>\n<p>A circle is the set of all points in a plane that are equidistant from a given point, called the <em>center<\/em>.<\/p>\n<p>A <em>radius<\/em> of a circle is a segment that joins the center of the circle to any point on the circle.<\/p>\n<p>A <em>diameter <\/em>of a circle is a segment that contains the center of the circle and whose endpoints lie on the circle.<\/p>\n<h3>Circumference<\/h3>\n<p>Recall that the perimeter of a figure is the distance around the figure. Well, <em>circumference<\/em> is just the perimeter of a circle. Like perimeter, the units of circumference are one-dimensional, like inches or centimeters.<\/p>\n<p>The circumference of a circle is given by the formula C = 2\u03c0r, where \u03c0 is the irrational number pi and r is the radius.<\/p>\n<p>Since the diameter of a circle is twice the radius (d = 2r), the formula C = \u03c0d is an equivalent formula. You may choose which formula to use based on the information that you\u2019re given.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the circumference of a circle of radius 8 m? Round your answer to the nearest meter.<\/p>\n<ol>\n<li>19 m<\/li>\n<li>25 m<\/li>\n<li>50 m<\/li>\n<li>101 m<\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice C is the correct answer. Since the radius of the circle is given, use the formula C = 2\u03c0r, where r = 8 m.<\/p>\n<p class=\"q-reveal\"><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/s13_p1_answer.gif\" alt=\"Answer formula\" \/><\/p>\n<\/section>\n<h3>Area<\/h3>\n<p>Recall that the area of a two-dimensional figure is the number of square units it contains. So, the area of a circle is given in units like in<sup>2<\/sup> or ft<sup>2<\/sup>.<\/p>\n<p>The area of a circle is given by the formula A = \u03c0r<sup>2<\/sup>, where r is the radius of the circle.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the area of this circle? Round your answer to the nearest square foot.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/circle.jpg\" alt=\"Circle question\" \/><\/center><\/p>\n<ol>\n<li>188 ft<sup>2<\/sup><\/li>\n<li>707 ft<sup>2<\/sup><\/li>\n<li>903 ft<sup>2<\/sup><\/li>\n<li>2826 ft<sup>2<\/sup><\/li>\n<\/ol>\n<p><a class=\"q-answer button button-primary\">Reveal Answer<\/a><\/p>\n<p class=\"q-reveal\">Choice B is correct. The area of the circle is given by the formula A = \u03c0r<sup>2<\/sup>. Since the diameter of the circle is 30 ft, the radius is 15 ft. If you answered C, you may have added p to the square of the radius rather than multiplying it. If you answered D, you may have used the diameter in the formula rather than the radius. So the area is:<\/p>\n<p class=\"q-reveal center\"><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/wp-content\/uploads\/sites\/4\/2017\/08\/6.3a_040.gif\" alt=\"Answer formula\" \/><\/p>\n<\/section>\n<h3>Review<\/h3>\n<ul>\n<li>The circumference of a circle is the distance around the circle. It is given by the formulas C = 2\u03c0r, where r is the radius, or C = \u03c0d, where d is the diameter.<\/li>\n<li>The area of a circle is given by the formula, A = \u03c0r<sup>2<\/sup>, where r is the radius of the circle.<\/li>\n<\/ul>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measuring-quadrilaterals\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/geometry-measurement\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/elementary-education\/measurements-involving-three-dimensional-figures\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Measuring Circles Objective In this lesson you will learn to find the circumference and area of a circle. Previously Covered Previously, we reviewed formulas to measure triangles and quadrilaterals. About Circles A circle is the set of all points in a plane that are equidistant from a given point, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-265","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/265","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/comments?post=265"}],"version-history":[{"count":7,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/265\/revisions"}],"predecessor-version":[{"id":1397,"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/pages\/265\/revisions\/1397"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/elementary-education\/wp-json\/wp\/v2\/media?parent=265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}