{"id":5388,"date":"2021-03-17T23:41:44","date_gmt":"2021-03-17T23:41:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/using-the-properties-of-circles-to-solve-problems-2\/"},"modified":"2022-03-01T01:15:24","modified_gmt":"2022-03-01T01:15:24","slug":"using-the-properties-of-circles-to-solve-problems-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/using-the-properties-of-circles-to-solve-problems-2\/","title":{"raw":"Using the Properties of Circles to Solve Problems","rendered":"Using the Properties of Circles to Solve Problems"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the circumference and area of a circular object given its radius or diameter<\/li>\r\n \t<li>Calculate the diameter or radius of a circular object given its circumference<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Properties of Circles<\/h3>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224027\/CNX_BMath_Figure_09_05_001.png\" alt=\"An image of a circle is shown. There is a line drawn through the widest part at the center of the circle with a red dot indicating the center of the circle. The line is labeled d. The two segments from the center of the circle to the outside of the circle are each labeled r.\" \/>\r\n<ul id=\"fs-id1489165\">\r\n \t<li>[latex]r[\/latex] is the length of the radius<\/li>\r\n \t<li>[latex]d[\/latex] is the length of the diameter<\/li>\r\n \t<li>[latex]d=2r[\/latex]<\/li>\r\n \t<li>Circumference is the perimeter of a circle. The formula for circumference is [latex]C=2\\pi r[\/latex]<\/li>\r\n \t<li>The formula for area of a circle is [latex]A=\\pi {r}^{2}[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe will use the pi button on your calculator to get exact answers to these questions and then round our final answers to the specified number of decimal places.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA circular sandbox has a radius of [latex]2.5[\/latex] feet. Find 1. the circumference and 2. the area of the sandbox.\u00a0 Round your answers to the nearest tenth.\r\n\r\nSolution\r\n<table id=\"eip-id1168467555346\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>1.\r\n\r\nStep 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224028\/CNX_BMath_Figure_09_05_029_img-01.png\" alt=\"Circle with radius of 2.5 ft.\" width=\"159\" height=\"159\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>The circumference of the circle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let <em>c<\/em> = circumference of the circle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula\r\n\r\nSubstitute<\/td>\r\n<td>[latex]C=2\\pi r[\/latex]\r\n\r\n[latex]C=2\\pi \\left(2.5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]C= 15.7 \\text{ft}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check.<\/strong> Does this answer make sense?\r\n\r\nYes. If we draw a square around the circle, its sides would be [latex]5[\/latex] ft (twice the radius), so its perimeter would be [latex]20[\/latex] ft. This is slightly more than the circle's circumference, [latex]15.7[\/latex] ft.\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224029\/CNX_BMath_Figure_09_05_029_img-02.png\" alt=\"A circle inside of a square.  The circle fits perfectly inside the square and touches on all four sides of the square.  Each side of the square is 5 ft.  The radius of the circle is 2.5 ft.\" width=\"206\" height=\"188\" \/><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The circumference of the sandbox is [latex]15.7 [\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468253524\" class=\"unnumbered unstyled\" summary=\"Identify what you are looking for.\">\r\n<tbody>\r\n<tr>\r\n<td>2.\r\n\r\nStep 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224028\/CNX_BMath_Figure_09_05_029_img-01.png\" alt=\"Circle with radius 2.5 feet\" width=\"159\" height=\"159\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>The area of the circle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let <em>A<\/em> = the area of the circle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula\r\n\r\nSubstitute<\/td>\r\n<td>[latex]A=\\pi {r}^{2}[\/latex]\r\n\r\n[latex]A=\\pi{\\left(2.5\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]A=19.6 \\text{sq. ft}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check.<\/strong>\r\n\r\nYes. If we draw a square around the circle, its sides would be [latex]5[\/latex] ft, as shown in part \u24d0. So the area of the square would be [latex]25[\/latex] sq. ft. This is slightly more than the circle's area, [latex]19.6[\/latex] sq. ft.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The area of the circle is [latex]19.6 [\/latex] square feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nIn the following video we show another example of how to find the area of a circle.\r\n\r\nhttps:\/\/youtu.be\/SIKkWLqt2mQ\r\n\r\nWe usually see the formula for circumference in terms of the radius [latex]r[\/latex] of the circle:\r\n\r\n[latex]C=2\\pi r[\/latex]\r\n\r\nBut since the diameter of a circle is two times the radius, we could write the formula for the circumference in terms [latex]\\text{of }d[\/latex].\r\n\r\n[latex]\\begin{array}{cccc}&amp; &amp; &amp; C=2\\pi r\\hfill \\\\ \\text{Using the commutative property, we get}\\hfill &amp; &amp; &amp; C=\\pi \\cdot 2r\\hfill \\\\ \\text{Then substituting }d=2r\\hfill &amp; &amp; &amp; C=\\pi \\cdot d\\hfill \\\\ \\text{So}\\hfill &amp; &amp; &amp; C=\\pi d\\hfill \\end{array}[\/latex]\r\n\r\nWe will use this form of the circumference when we\u2019re given the length of the diameter instead of the radius.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA circular table has a diameter of four feet. What is the circumference of the table? Round your answer to the nearest hundredth.\r\n[reveal-answer q=\"808290\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"808290\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467247251\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224030\/CNX_BMath_Figure_09_05_032_img-01.png\" alt=\"A circle with a diameter of 4 feet\" width=\"230\" height=\"227\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>The circumference of the table<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let C = the circumference of the table<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula for the situation.\r\n\r\nSubstitute.<\/td>\r\n<td>[latex]C=\\pi d[\/latex]\r\n\r\n[latex]C=\\pi \\left(4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]C = 12.57 \\text{feet}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> If we put a square around the circle, its side would be [latex]4[\/latex].\r\n\r\nThe perimeter would be [latex]16[\/latex]. It makes sense that the circumference of the circle, [latex]12.56[\/latex], is a little less than [latex]16[\/latex].\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224032\/CNX_BMath_Figure_09_05_032_img-02.png\" alt=\"A circle inscribed in a square.  Each side of the square is 4 ft.  The diameter of the circle is 4 ft.\" width=\"294\" height=\"270\" \/><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The diameter of the table is [latex]12.57 [\/latex] square feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the next video we show two more examples of how to find the circumference of a circle given its diameter, or its radius.\r\n\r\nhttps:\/\/youtu.be\/sHtsnC2Mgnk\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the diameter of a circle with a circumference of [latex]47.1[\/latex] centimeters.\u00a0 Round your answer to the nearest whole number.\r\n[reveal-answer q=\"282807\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282807\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468767882\" class=\"unnumbered unstyled\" style=\"height: 722px;\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr style=\"height: 286px;\">\r\n<td style=\"height: 286px; width: 380.979px;\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td style=\"height: 286px; width: 288.979px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224033\/CNX_BMath_Figure_09_05_033_img-01.png\" alt=\"A circle with diameter labelled d.  C = 47.1 cm is given.\" width=\"218\" height=\"239\" \/>\r\n\r\n[latex]C=47.1[\/latex]cm<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 380.979px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td style=\"height: 11px; width: 288.979px;\">The diameter of the circle<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 380.979px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td style=\"height: 11px; width: 288.979px;\">Let [latex]d[\/latex]\u00a0= the diameter of the circle<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 380.979px;\">Step 4. <strong>Translate.<\/strong><\/td>\r\n<td style=\"height: 11px; width: 288.979px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 90px;\">\r\n<td style=\"height: 90px; width: 380.979px;\">Write the formula.\r\n\r\nSubstitute.<\/td>\r\n<td style=\"height: 90px; width: 288.979px;\">[latex]C=\\pi{d}[\/latex]\r\n\r\n[latex]47.1\\approx\\pi{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 132px;\">\r\n<td style=\"height: 132px; width: 380.979px;\">Step 5. <strong>Solve.<\/strong><\/td>\r\n<td style=\"height: 132px; width: 288.979px;\">[latex]\r\n\r\n\\Large\\frac{47.1}{\\pi}\\normalsize\\approx\r\n\r\n\\Large\\frac{\\pi d}{\\pi}[\/latex]\r\n\r\n[latex]15\\approx{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 157px;\">\r\n<td style=\"height: 157px; width: 380.979px;\">Step 6. <strong>Check:<\/strong>\r\n\r\n<strong>[latex]C=\\pi{d}[\/latex]<\/strong>\r\n\r\n[latex]47.1\\stackrel{?}{=}\\left(\\pi\\right)\\left(15\\right)[\/latex]\r\n\r\n[latex]47.1=47.1\\quad\\checkmark [\/latex]<\/td>\r\n<td style=\"height: 157px; width: 288.979px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px;\">\r\n<td style=\"height: 24px; width: 380.979px;\">Step 7. <strong>Answer the question.<\/strong><\/td>\r\n<td style=\"height: 24px; width: 288.979px;\">The diameter of the circle is approximately [latex]15[\/latex] centimeters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the circumference and area of a circular object given its radius or diameter<\/li>\n<li>Calculate the diameter or radius of a circular object given its circumference<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Properties of Circles<\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224027\/CNX_BMath_Figure_09_05_001.png\" alt=\"An image of a circle is shown. There is a line drawn through the widest part at the center of the circle with a red dot indicating the center of the circle. The line is labeled d. The two segments from the center of the circle to the outside of the circle are each labeled r.\" \/><\/p>\n<ul id=\"fs-id1489165\">\n<li>[latex]r[\/latex] is the length of the radius<\/li>\n<li>[latex]d[\/latex] is the length of the diameter<\/li>\n<li>[latex]d=2r[\/latex]<\/li>\n<li>Circumference is the perimeter of a circle. The formula for circumference is [latex]C=2\\pi r[\/latex]<\/li>\n<li>The formula for area of a circle is [latex]A=\\pi {r}^{2}[\/latex]<\/li>\n<\/ul>\n<\/div>\n<p>We will use the pi button on your calculator to get exact answers to these questions and then round our final answers to the specified number of decimal places.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A circular sandbox has a radius of [latex]2.5[\/latex] feet. Find 1. the circumference and 2. the area of the sandbox.\u00a0 Round your answers to the nearest tenth.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467555346\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>1.<\/p>\n<p>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224028\/CNX_BMath_Figure_09_05_029_img-01.png\" alt=\"Circle with radius of 2.5 ft.\" width=\"159\" height=\"159\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>The circumference of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em>c<\/em> = circumference of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula<\/p>\n<p>Substitute<\/td>\n<td>[latex]C=2\\pi r[\/latex]<\/p>\n<p>[latex]C=2\\pi \\left(2.5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]C= 15.7 \\text{ft}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check.<\/strong> Does this answer make sense?<\/p>\n<p>Yes. If we draw a square around the circle, its sides would be [latex]5[\/latex] ft (twice the radius), so its perimeter would be [latex]20[\/latex] ft. This is slightly more than the circle&#8217;s circumference, [latex]15.7[\/latex] ft.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224029\/CNX_BMath_Figure_09_05_029_img-02.png\" alt=\"A circle inside of a square.  The circle fits perfectly inside the square and touches on all four sides of the square.  Each side of the square is 5 ft.  The radius of the circle is 2.5 ft.\" width=\"206\" height=\"188\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The circumference of the sandbox is [latex]15.7[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468253524\" class=\"unnumbered unstyled\" summary=\"Identify what you are looking for.\">\n<tbody>\n<tr>\n<td>2.<\/p>\n<p>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224028\/CNX_BMath_Figure_09_05_029_img-01.png\" alt=\"Circle with radius 2.5 feet\" width=\"159\" height=\"159\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>The area of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em>A<\/em> = the area of the circle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula<\/p>\n<p>Substitute<\/td>\n<td>[latex]A=\\pi {r}^{2}[\/latex]<\/p>\n<p>[latex]A=\\pi{\\left(2.5\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]A=19.6 \\text{sq. ft}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check.<\/strong><\/p>\n<p>Yes. If we draw a square around the circle, its sides would be [latex]5[\/latex] ft, as shown in part \u24d0. So the area of the square would be [latex]25[\/latex] sq. ft. This is slightly more than the circle&#8217;s area, [latex]19.6[\/latex] sq. ft.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The area of the circle is [latex]19.6[\/latex] square feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>In the following video we show another example of how to find the area of a circle.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example:  Determine the Area of a Circle\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SIKkWLqt2mQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>We usually see the formula for circumference in terms of the radius [latex]r[\/latex] of the circle:<\/p>\n<p>[latex]C=2\\pi r[\/latex]<\/p>\n<p>But since the diameter of a circle is two times the radius, we could write the formula for the circumference in terms [latex]\\text{of }d[\/latex].<\/p>\n<p>[latex]\\begin{array}{cccc}& & & C=2\\pi r\\hfill \\\\ \\text{Using the commutative property, we get}\\hfill & & & C=\\pi \\cdot 2r\\hfill \\\\ \\text{Then substituting }d=2r\\hfill & & & C=\\pi \\cdot d\\hfill \\\\ \\text{So}\\hfill & & & C=\\pi d\\hfill \\end{array}[\/latex]<\/p>\n<p>We will use this form of the circumference when we\u2019re given the length of the diameter instead of the radius.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A circular table has a diameter of four feet. What is the circumference of the table? Round your answer to the nearest hundredth.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q808290\">Show Solution<\/span><\/p>\n<div id=\"q808290\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467247251\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224030\/CNX_BMath_Figure_09_05_032_img-01.png\" alt=\"A circle with a diameter of 4 feet\" width=\"230\" height=\"227\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>The circumference of the table<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let C = the circumference of the table<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula for the situation.<\/p>\n<p>Substitute.<\/td>\n<td>[latex]C=\\pi d[\/latex]<\/p>\n<p>[latex]C=\\pi \\left(4\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]C = 12.57 \\text{feet}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> If we put a square around the circle, its side would be [latex]4[\/latex].<\/p>\n<p>The perimeter would be [latex]16[\/latex]. It makes sense that the circumference of the circle, [latex]12.56[\/latex], is a little less than [latex]16[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224032\/CNX_BMath_Figure_09_05_032_img-02.png\" alt=\"A circle inscribed in a square.  Each side of the square is 4 ft.  The diameter of the circle is 4 ft.\" width=\"294\" height=\"270\" \/><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The diameter of the table is [latex]12.57[\/latex] square feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>In the next video we show two more examples of how to find the circumference of a circle given its diameter, or its radius.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Determine the Circumference of a Circle\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/sHtsnC2Mgnk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the diameter of a circle with a circumference of [latex]47.1[\/latex] centimeters.\u00a0 Round your answer to the nearest whole number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q282807\">Show Solution<\/span><\/p>\n<div id=\"q282807\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468767882\" class=\"unnumbered unstyled\" style=\"height: 722px;\" summary=\"Step 1 says,\">\n<tbody>\n<tr style=\"height: 286px;\">\n<td style=\"height: 286px; width: 380.979px;\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td style=\"height: 286px; width: 288.979px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224033\/CNX_BMath_Figure_09_05_033_img-01.png\" alt=\"A circle with diameter labelled d.  C = 47.1 cm is given.\" width=\"218\" height=\"239\" \/><\/p>\n<p>[latex]C=47.1[\/latex]cm<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 380.979px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td style=\"height: 11px; width: 288.979px;\">The diameter of the circle<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 380.979px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"height: 11px; width: 288.979px;\">Let [latex]d[\/latex]\u00a0= the diameter of the circle<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 380.979px;\">Step 4. <strong>Translate.<\/strong><\/td>\n<td style=\"height: 11px; width: 288.979px;\"><\/td>\n<\/tr>\n<tr style=\"height: 90px;\">\n<td style=\"height: 90px; width: 380.979px;\">Write the formula.<\/p>\n<p>Substitute.<\/td>\n<td style=\"height: 90px; width: 288.979px;\">[latex]C=\\pi{d}[\/latex]<\/p>\n<p>[latex]47.1\\approx\\pi{d}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 132px;\">\n<td style=\"height: 132px; width: 380.979px;\">Step 5. <strong>Solve.<\/strong><\/td>\n<td style=\"height: 132px; width: 288.979px;\">[latex]\\Large\\frac{47.1}{\\pi}\\normalsize\\approx    \\Large\\frac{\\pi d}{\\pi}[\/latex]<\/p>\n<p>[latex]15\\approx{d}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 157px;\">\n<td style=\"height: 157px; width: 380.979px;\">Step 6. <strong>Check:<\/strong><\/p>\n<p><strong>[latex]C=\\pi{d}[\/latex]<\/strong><\/p>\n<p>[latex]47.1\\stackrel{?}{=}\\left(\\pi\\right)\\left(15\\right)[\/latex]<\/p>\n<p>[latex]47.1=47.1\\quad\\checkmark[\/latex]<\/td>\n<td style=\"height: 157px; width: 288.979px;\"><\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"height: 24px; width: 380.979px;\">Step 7. <strong>Answer the question.<\/strong><\/td>\n<td style=\"height: 24px; width: 288.979px;\">The diameter of the circle is approximately [latex]15[\/latex] centimeters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-5388\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146787, 146786, 146785. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Examples: Determine the Circumference of a Circle. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/sHtsnC2Mgnk\">https:\/\/youtu.be\/sHtsnC2Mgnk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Example: Determine the Area of a Circle. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/SIKkWLqt2mQ\">https:\/\/youtu.be\/SIKkWLqt2mQ<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146787, 146786, 146785\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Examples: Determine the Circumference of a Circle\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/sHtsnC2Mgnk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example: Determine the Area of a Circle\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/SIKkWLqt2mQ\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"02d08692a6434bdc94f5af873d12a3de, 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