{"id":21728,"date":"2016-02-17T22:45:30","date_gmt":"2016-02-17T22:45:30","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=21728"},"modified":"2026-03-28T11:23:12","modified_gmt":"2026-03-28T16:23:12","slug":"the-diameter-radius-and-circumference-of-circles","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/the-diameter-radius-and-circumference-of-circles\/","title":{"rendered":"The Diameter, Radius, and Circumference of&nbsp;Circles"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_iwTkd0ieAzI\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_iwTkd0ieAzI\" data-source-videoID=\"iwTkd0ieAzI\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"The Diameter, Radius, and Circumference of&nbsp;Circles Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"The Diameter, Radius, and Circumference of&nbsp;Circles\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_iwTkd0ieAzI:hover {cursor:pointer;} img#videoThumbnailImage_iwTkd0ieAzI {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/112-the-diameter-radius-and-circumference-of-circles-2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_iwTkd0ieAzI\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_iwTkd0ieAzI\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"The Diameter, Radius, and Circumference of&nbsp;Circles\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_iwTkd0ieAzI\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_iwTkd0ieAzI\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_iwTkd0ieAzI\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction b7y_Function() {\n  var x = document.getElementById(\"b7y\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"b7y_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"b7y\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#A_Quick_History_of_Circles\" class=\"smooth-scroll\">A Quick History of Circles<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Radius_vs_Diameter\" class=\"smooth-scroll\">Radius vs. Diameter<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Calculations\" class=\"smooth-scroll\">Calculations<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Circle_Practice_Questions\" class=\"smooth-scroll\">Circle Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label><a href=\"https:\/\/www.mometrix.com\/academy\/area-of-a-circle-calculator\/\" target=\"none\" style=\"margin: 0 auto;\"><span class=\"accordion_calculator_button\">Calculator<\/span><\/a><\/p>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey guys! Welcome to this video on the radius, diameter, and circumference of a circle.<\/p>\n<h2><span id=\"A_Quick_History_of_Circles\" class=\"m-toc-anchor\"><\/span>A Quick History of Circles<\/h2>\n<p>\nCircles have been around for as long as the Earth has been around. People were able to see natural circles by observing the moon, the sun, and other various naturally circular shapes.<\/p>\n<p>The first technological invention using a circular shape, however, wasn\u2019t until 3500 BC, and it was the invention of the potter\u2019s wheel. Then, 300 years later, they were used for the wheels of chariots. As people began to see the value and use for circular-shaped objects, they begin to study circles.<\/p>\n<p>Things like <em>radius<\/em>, <em>diameter<\/em>, and <em>circumference<\/em> are terms that helps us to keep track of various measurements of a circle.<\/p>\n<p>So, now, let\u2019s take a look what each of these measurements represent.<\/p>\n<h3><span id=\"Midpoint_of_a_Circle\" class=\"m-toc-anchor\"><\/span>Midpoint of a Circle<\/h3>\n<p>\nFirst, let\u2019s define <strong>midpoint<\/strong>, so you\u2019ll understand what I\u2019m talking about as I reference it. Here&#8217;s a circle:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/midpoint-circle-09.svg\" alt=\"\" width=\"307.396\" height=\"309.039\" class=\"aligncenter size-full wp-image-198476\"  role=\"img\" \/><\/p>\n<p>The midpoint is the exact center of the circle, where the dot is.<\/p>\n<h2><span id=\"Radius_vs_Diameter\" class=\"m-toc-anchor\"><\/span>Radius vs. Diameter<\/h2>\n<h3><span id=\"Radius_of_a_Circle\" class=\"m-toc-anchor\"><\/span>Radius of a Circle<\/h3>\n<p>\nRadius is the length from the midpoint of the circle to the outer edge of the circle. The radius is represented by the lowercase letter \\(r\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/radius-of-a-circle-09.svg\" alt=\"\" width=\"307.396\" height=\"309.039\" class=\"aligncenter size-full wp-image-198470\"  role=\"img\" \/><\/p>\n<h3><span id=\"Diameter_of_a_Circle\" class=\"m-toc-anchor\"><\/span>Diameter of a Circle<\/h3>\n<p>\nDiameter is the full length of the circle running from the edge, through the midpoint, all the way to the other side. That is this whole length right here. The diameter of a circle is represented by the letter \\(d\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/circle-diameter-09.svg\" alt=\"\" width=\"307.396\" height=\"309.039\" class=\"aligncenter size-full wp-image-198479\"  role=\"img\" \/><\/p>\n<h3><span id=\"Circumference_of_a_Circle\" class=\"m-toc-anchor\"><\/span>Circumference of a Circle<\/h3>\n<p>\nNow, circumference is the distance around the outside edge of this circle. Circumference is represented by the uppercase letter \\(C\\).<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/circle-circumference-09.svg\" alt=\"\" width=\"307.396\" height=\"309.039\" class=\"aligncenter size-full wp-image-198482\"  role=\"img\" \/><\/p>\n<p>Circumference is comparable to the perimeter of a shape, like a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/area-and-perimeter-of-a-parallelogram\/\">parallelogram<\/a>. If you were to cut the line of a circle, as if it were a string, and lay it out to measure. This length would be equivalent to the circumference. However, since a circle has a continuous curve, we use the word <em>circumference<\/em> rather than <em>perimeter<\/em> to distinguish it.<\/p>\n<p>Now that we\u2019ve looked at what the radius, diameter, and circumference are, let\u2019s look at how to calculate each one.<\/p>\n<h2><span id=\"Calculations\" class=\"m-toc-anchor\"><\/span>Calculations<\/h2>\n<p>\nIf someone were to just kinda hand you a piece of paper with a circle on it\u2026. Well, actually, that would be pretty weird.<\/p>\n<p>But let\u2019s say we wanted to find the radius, diameter, and circumference of that circle, and all we have is a ruler.<\/p>\n<p>The easiest thing to start with would be to take the ruler and measure, from the very center of the circle, the length between the outer edge. That would be the diameter.<\/p>\n<p>Let\u2019s say, that when we measured, we got a length of 9 cm for the diameter. <\/p>\n<p>Well, we know that if our radius runs from the midpoint to the outer edge, then all we have to do to find the length of our radius would be to divide the length of the diameter by 2.<\/p>\n<p>So, when we take 9 and divide it by 2 we get a radius length of 4.5 cm.<\/p>\n<h3><span id=\"Radius_Formula\" class=\"m-toc-anchor\"><\/span>Radius Formula<\/h3>\n<p>The formula for the radius can be written as \\(r=\\frac{d}{2}\\)<\/p>\n<h3><span id=\"Diameter_Formula\" class=\"m-toc-anchor\"><\/span>Diameter Formula<\/h3>\n<p>The formula for diameter can be written as \\(d=2r\\)<\/p>\n<h3><span id=\"Circumference_Formula\" class=\"m-toc-anchor\"><\/span>Circumference Formula<\/h3>\n<p>The formula for the circumference of a circle is \\(C=\\pi \\times d\\), or it can be written as \\(C=2\\times \\pi \\times r\\). Either one works!<\/p>\n<p>Now, you may be asking, &#8220;Well where did pi come from, and why do we all the sudden get the circumference if we multiply said pi by our diameter? Who decided that?\u201d If you are not asking that question\u2026 You should, and I\u2019m going to answer it anyways.<\/p>\n<p><strong>Pi<\/strong> is a symbol we use in mathematics to represent the number 3.14. And actually that is just pi rounded to the nearest hundredth. Pi actually has no end, and no predictable pattern. It just keeps going.<\/p>\n<p>However, when you see the symbol \\(\\pi\\), generally (and in our case), 3.14 will suffice.<\/p>\n<p>Pi is not a random number that mathematicians made up, and declared \u201cwe will multiply the diameter by the number every time, and call it a circumference.\u201d On the contrary, pi was discovered to be the constant <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/ratios\/\">ratio<\/a> between the circumference and the diameter.<\/p>\n<p>That is why and how we got the formula for the circumference of a circle.<\/p>\n<p>Now, let\u2019s take the circle with the diameter of 9 cm, and radius of 4.5 cm, and calculate the circumference.<\/p>\n<p>I\u2019m going to use the formula with the diameter for this one.<\/p>\n<p>So, circumference equals (I&#8217;m just gonna rewrite the formula to help us follow our work), \\(C=\\pi \\times d\\), equals pi times diameter. So now all we need to do is to plug in our number for diameter.<\/p>\n<p>\\(C=(3.14)(9\\text{ cm})=28.26\\text{ cm}\\)<br \/>\n&nbsp;<br \/>\nAnd here&#8217;s our answer! Now to practice, try drawing a circle on a piece of paper, and measure your diameter with a ruler. Then, find your radius, and circumference.<\/p>\n<p>I hope that this video has been helpful for you.<\/p>\n<p>See you guys next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the radius of a circle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>If we were to measure the distance running from the center of a circle to the outer edge of said circle, we would be finding the radius.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/radius-of-a-circle-09.svg\" alt=\"An example of the radius of a circle.\" width=\"210\" height=\"210\" class=\"aligncenter size-full wp-image-198470\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What are radius and diameter?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>While the radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center. A circle\u2019s diameter essentially splits the shape in half.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/circle-diameter-09.svg\" alt=\"Example of a diameter of a circle.\" width=\"210\" height=\"210\" class=\"aligncenter size-full wp-image-198479\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Is a radius half the diameter?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Yes! A radius is half the length of the diameter.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Radius-and-Diameter.svg\" alt=\"A circle with a labeled diameter &quot;d&quot; in orange, a labeled radius &quot;r&quot; in blue, and a black dot marking the center.\" width=\"210\" height=\"210\" class=\"aligncenter size-full wp-image-286840\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you solve for radius and diameter?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>If you only know the radius of a circle, just multiply that value by 2 in order to get the diameter (\\(d=2r\\)). Similarly, if you only know the diameter of a circle, divide by 2 to get the radius (\\(r=\\frac{d}{2}\\)).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do you calculate the circumference of a circle?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>In order to calculate a circle\u2019s circumference, we need to know either its diameter or its radius. We then use the appropriate value in the equation \\(C=2\\pi r\\). <\/p>\n<div class=\"lightbulb-example-2\" style=\"min-width: 70%\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Find the circumference of this circle:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/10-cm-Diameter.svg\" alt=\"A circle with a horizontal orange line labeled &quot;10 cm&quot; representing the diameter.\" width=\"178\" height=\"178\" class=\"aligncenter size-full wp-image-286843\"  role=\"img\" \/><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">\n<p style=\"text-align: center; line-height: 55px; margin-bottom: -0.5em\">\\(r=\\dfrac{10\\mathrm{\\:cm}}{2}=5\\mathrm{\\:cm}\\)<br \/>\\(C=2\\pi r=2\\pi \\times 5=10\\pi \\mathrm{\\:cm}\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Why is circumference \\(2\\pi r\\)?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>We know that circumference is the length of the entire outer edge of a circle.<\/p>\n<p>With this in mind, rearrange the variables in the equation \\(C=2\\pi r\\) to get \\(C=2r\\times \\pi\\). Remember that \\(2r=d\\), so we could rewrite this equation yet again as \\(C=d\\times \\pi\\).<\/p>\n<p>In other words, we can wrap a string (which is the same length as the diameter) around the circle 3.1415926\u2026 times.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Diameter-and-Circumference.svg\" alt=\"A circle with a center dot, marked radius points on the circumference, and a curved dashed line labeled &quot;d&quot; along the edge.\" width=\"210.56\" height=\"206.08\" class=\"aligncenter size-full wp-image-286849\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">How do we use circumference in everyday life?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The applications of circumference in everyday life are truly endless!<\/p>\n<p>One example, though, is determining how large of a tire someone needs for a bike or for a car.<\/p>\n<p>Another example would be finding how much wood is in a tree. With a very, very old tree, it would be pretty difficult to measure the diameter of the tree\u2019s base, but it would be straightforward to wrap a rope around the base and measure the circumference. Then, you could use this circumference measurement and reverse-engineer the circumference equation to determine the tree\u2019s diameter. With this measurement (and the height of the tree), we could find the volume of wood within this tree.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is circumference vs. diameter?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Circumference is the length of one complete &#8220;lap&#8221; around a circle, and diameter is the length of the line segment that cuts a circle in half. Think of circumference as an outer measurement and diameter as an inner measurement of the circle!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Circumference-and-Diameter.svg\" alt=\"A circle with center dot, a diameter labeled &quot;d,&quot; and the circumference traced with a dashed green line labeled &quot;C.\" width=\"210\" height=\"210\" class=\"aligncenter size-full wp-image-286852\"  role=\"img\" \/><\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Is diameter half the circumference?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>No! Remember the equation \\(C=2\\pi r\\) can be rewritten: \\(C=2r\\times \\pi\\), \\(C=d\\times \\pi\\), or \\(C=\\pi d\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Is a diameter a length?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>If length is defined as the distance between two points, then yes, diameter is a length. The diameter of a circle measures the distance between the two furthest points on a circle.<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Circle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Circle Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nDetermine the circumference of the circle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/8-cm-Diameter.svg\" alt=\"A circle with a horizontal line labeled &quot;8 cm&quot; representing the diameter.\" width=\"190\" height=\"190\" class=\"aligncenter size-full wp-image-286855\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">23.16 cm<\/div><div class=\"PQ\"  id=\"PQ-1-2\">24.14 cm<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">25.12 cm<\/div><div class=\"PQ\"  id=\"PQ-1-4\">26.11 cm<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The circumference of a circle can be calculated using either \\(C=\\pi d\\) or \\(C=2\\pi r\\).<\/p>\n<p>We know that the diameter of the circle is 8 cm, and an approximation for pi is 3.14, so we can plug these values into the formula \\(C= \\pi d\\). The formula becomes \\(C=(3.14)(8)\\), which simplifies to 25.12.<\/p>\n<p>Therefore, the circumference of the circle is 25.12 cm.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nDetermine the radius of the circle if the circumference is twenty-three inches. Round your answer to the nearest hundredths.<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">3.66 inches<\/div><div class=\"PQ\"  id=\"PQ-2-2\">4.65 inches<\/div><div class=\"PQ\"  id=\"PQ-2-3\">3.44 inches<\/div><div class=\"PQ\"  id=\"PQ-2-4\">4.76 inches<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The radius of a circle can be calculated if the circumference is known. We know that the circumference of the circle is 23 inches, so we can plug this into the formula \\(C=2\\pi r\\).<\/p>\n<p>We also know that an approximation of pi is 3.14, so the only value we do not know is the radius. When \\(C\\) and \\(\\pi\\) are plugged into the formula, it becomes \\(23=2(3.14)r\\). This can be simplified to \\(23=6.28r\\), and then both sides of the equation can be divided by 6.28 in order to isolate the variable \\(r\\). <\/p>\n<p style=\"text-align: center\">\\(23 \\div 6.28 = 3.66\\)<\/p>\n<p>Therefore, the radius of the circle is 3.66 inches.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nIf \\(C\\) represents circumference, \\(r\\) represents radius, and \\(d\\) represents diameter, which formula is incorrect? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(d=2r\\) <\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(C=\\pi d\\) <\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(C=2\\pi r\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(r=\\pi dC\\) <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Multiplying pi, times diameter, times circumference does not equal the radius. If the diameter is known, then the radius is simply half the value of \\(d\\). <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nBicycles from the 1800s look very different from the bikes we see today. In the photograph below, the bicycle\u2019s back wheel has a radius of 9 inches, and the front wheel has a diameter of 60 inches. Using 3.14 as an approximation for pi, what is the difference between the circumference of the front and back wheel? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-70787 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle.png\" alt=\"Old bicycle\" width=\"167\" height=\"243\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle.png 1951w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle-206x300.png 206w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle-705x1024.png 705w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle-768x1116.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle-1057x1536.png 1057w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/Old-bicycle-1409x2048.png 1409w\" sizes=\"auto, (max-width: 167px) 100vw, 167px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">161.88 inches<\/div><div class=\"PQ\"  id=\"PQ-4-2\">151.88 inches<\/div><div class=\"PQ\"  id=\"PQ-4-3\">171.88 inches<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">131.88 inches<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Before comparing the front and back wheel, we need to calculate the circumference of each wheel individually.<\/p>\n<p>The circumference of a circle can be found using the formula \\(C=2\\pi r\\) or \\(C=\\pi d\\). We know the radius of the back wheel is 9 inches, so we can plug this into the formula \\(C=2\\pi r\\). The formula becomes \\(C=2\\pi (9)\\) which simplifies to 56.52.<\/p>\n<p>The front tire has a diameter of 60 inches so we can plug this into the formula \\(C=\\pi d\\). The formula becomes \\(C=\\pi (60)\\) which simplifies 188.4.<\/p>\n<p>Now that we know the circumference of each wheel we can simply subtract 56.52 from 188.4. The difference in the wheel circumferences is 131.88 inches.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nLauren is planning her trip to London, and she wants to take a ride on the famous Ferris wheel called the London Eye. While researching facts about the giant Ferris wheel, she learns that the radius of the circle measures approximately 68 meters. What is the approximate circumference of the Ferris wheel? Use 3.14 as an approximation for pi. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">427 meters<\/div><div class=\"PQ\"  id=\"PQ-5-2\">488 meters<\/div><div class=\"PQ\"  id=\"PQ-5-3\">407 meters<\/div><div class=\"PQ\"  id=\"PQ-5-4\">498 meters<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The formula \\(C=2\\pi r\\) can be used to calculate the circumference of the Ferris wheel. We can plug in 68 for the radius, and 3.14 as an approximation for pi.<\/p>\n<p>The formula \\(C=2\\pi r\\) becomes \\(C=2(3.14)(68)\\) which simplifies to 427.04, or approximately 427 meters.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":91126,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-21728","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-area-and-perimeter-videos","7":"page_category-circle-video","8":"page_category-math-advertising-group","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21728","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=21728"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21728\/revisions"}],"predecessor-version":[{"id":198467,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/21728\/revisions\/198467"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91126"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=21728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}