{"id":42127,"date":"2025-06-28T13:52:44","date_gmt":"2025-06-28T13:52:44","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42127"},"modified":"2025-06-28T13:52:45","modified_gmt":"2025-06-28T13:52:45","slug":"what-is-the-length-of-arc-ac-to-the-nearest-tenth-of-a-centimeter-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-length-of-arc-ac-to-the-nearest-tenth-of-a-centimeter-2\/","title":{"rendered":"What is the length of Arc AC to the nearest tenth of a centimeter"},"content":{"rendered":"\n<p>Circle B below has a radius of 10.5 centimeters and<br>. What is the length of Arc AC to the nearest tenth of a centimeter?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"527\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-451.png\" alt=\"\" class=\"wp-image-42128\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-451.png 683w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-451-300x231.png 300w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the length of Arc AC in Circle B, we use the arc length formula:<\/p>\n\n\n\n<p>Arc&nbsp;length=(\u03b8360)\u00d72\u03c0r\\text{Arc length} = \\left(\\frac{\\theta}{360}\\right) \\times 2\\pi r<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Radius r=10.5r = 10.5 cm<\/li>\n\n\n\n<li>Central angle \u03b8=18\u2218\\theta = 18^\\circ<\/li>\n<\/ul>\n\n\n\n<p>Substitute the values into the formula:<\/p>\n\n\n\n<p>Arc&nbsp;length=(18360)\u00d72\u03c0\u00d710.5\\text{Arc length} = \\left(\\frac{18}{360}\\right) \\times 2\\pi \\times 10.5<\/p>\n\n\n\n<p>=(120)\u00d72\u03c0\u00d710.5= \\left(\\frac{1}{20}\\right) \\times 2\\pi \\times 10.5<\/p>\n\n\n\n<p>=21\u03c020= \\frac{21\\pi}{20}<\/p>\n\n\n\n<p>Using \u03c0\u22483.1416\\pi \\approx 3.1416:<\/p>\n\n\n\n<p>Arc&nbsp;length\u224821\u00d73.141620\u224865.973620\u22483.3&nbsp;cm\\text{Arc length} \\approx \\frac{21 \\times 3.1416}{20} \\approx \\frac{65.9736}{20} \\approx 3.3 \\text{ cm}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>The length of Arc AC is approximately 3.3 centimeters.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>To determine the length of an arc in a circle, we rely on a fundamental geometric relationship that connects the arc length to the central angle and the radius. The arc length is a portion of the circle&#8217;s circumference, and its size depends on how large the central angle is compared to a full circle. A full circle has 360 degrees, so if the central angle is a fraction of that, the arc length is the same fraction of the total circumference.<\/p>\n\n\n\n<p>In this problem, Circle B has a radius of 10.5 centimeters and a central angle of 18 degrees. The formula for arc length is:<\/p>\n\n\n\n<p>Arc&nbsp;length=(\u03b8360)\u00d72\u03c0r\\text{Arc length} = \\left(\\frac{\\theta}{360}\\right) \\times 2\\pi r<\/p>\n\n\n\n<p>This formula calculates what fraction of the full circumference the arc represents. The term 2\u03c0r2\\pi r gives the total circumference of the circle, and multiplying it by \u03b8360\\frac{\\theta}{360} scales it down to the arc&#8217;s portion.<\/p>\n\n\n\n<p>By substituting the given values into the formula, we find that the arc length is approximately 3.3 centimeters. This result makes sense because 18 degrees is a small angle, and the arc it subtends should be a small portion of the circle\u2019s perimeter.<\/p>\n\n\n\n<p>This type of calculation is not only useful in geometry but also in real-world applications such as engineering, architecture, and design. Whether you&#8217;re measuring the curved edge of a mechanical part or designing a circular track, understanding how to compute arc lengths is essential. It demonstrates how mathematical principles translate into practical tools for solving spatial problems.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1392.jpeg\" alt=\"\" class=\"wp-image-42129\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1392.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1392-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1392-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Circle B below has a radius of 10.5 centimeters and. What is the length of Arc AC to the nearest tenth of a centimeter? The Correct Answer and Explanation is: To find the length of Arc AC in Circle B, we use the arc length formula: Arc&nbsp;length=(\u03b8360)\u00d72\u03c0r\\text{Arc length} = \\left(\\frac{\\theta}{360}\\right) \\times 2\\pi r Given: Substitute [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-42127","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=42127"}],"version-history":[{"count":2,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42127\/revisions"}],"predecessor-version":[{"id":42131,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42127\/revisions\/42131"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}