{"id":250339,"date":"2025-07-10T08:56:19","date_gmt":"2025-07-10T08:56:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=250339"},"modified":"2025-07-10T08:56:21","modified_gmt":"2025-07-10T08:56:21","slug":"a-78-rpm-record-turns-at-the-rate-of-78-revolutions-per-minute-as-its-name-implies","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/a-78-rpm-record-turns-at-the-rate-of-78-revolutions-per-minute-as-its-name-implies\/","title":{"rendered":"A 78-rpm record turns at the rate of 78 revolutions per minute, as its name implies."},"content":{"rendered":"\n<p>A 78-rpm record turns at the rate of 78 revolutions per minute, as its name implies. Through what angle (in radians) would such a record turn during a song that lasted for 3 minutes and 15 seconds?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to determine how many radians the record turns during the duration of the song. Here&#8217;s how we approach it:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Understand the given data<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The record turns at 78 revolutions per minute (rpm).<\/li>\n\n\n\n<li>The duration of the song is 3 minutes and 15 seconds. First, we need to convert this into a uniform unit of time, which is minutes.<\/li>\n<\/ul>\n\n\n\n<p>3&nbsp;minutes+15&nbsp;seconds=3&nbsp;minutes+1560&nbsp;minutes=3.25&nbsp;minutes3 \\text{ minutes} + 15 \\text{ seconds} = 3 \\text{ minutes} + \\frac{15}{60} \\text{ minutes} = 3.25 \\text{ minutes}3&nbsp;minutes+15&nbsp;seconds=3&nbsp;minutes+6015\u200b&nbsp;minutes=3.25&nbsp;minutes<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the number of revolutions in 3.25 minutes<\/h3>\n\n\n\n<p>Since the record turns at 78 rpm, the number of revolutions in 3.25 minutes is:Number&nbsp;of&nbsp;revolutions=78\u00d73.25=253.5&nbsp;revolutions\\text{Number of revolutions} = 78 \\times 3.25 = 253.5 \\text{ revolutions}Number&nbsp;of&nbsp;revolutions=78\u00d73.25=253.5&nbsp;revolutions<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Convert revolutions to radians<\/h3>\n\n\n\n<p>One full revolution corresponds to an angle of 2\u03c02\\pi2\u03c0 radians. Therefore, to find the total angle in radians, we multiply the number of revolutions by 2\u03c02\\pi2\u03c0:Angle&nbsp;in&nbsp;radians=253.5\u00d72\u03c0=253.5\u00d76.2832\u22481597.23&nbsp;radians\\text{Angle in radians} = 253.5 \\times 2\\pi = 253.5 \\times 6.2832 \\approx 1597.23 \\text{ radians}Angle&nbsp;in&nbsp;radians=253.5\u00d72\u03c0=253.5\u00d76.2832\u22481597.23&nbsp;radians<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The record turns through approximately <strong>1597.23 radians<\/strong> during the song that lasts 3 minutes and 15 seconds.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-107.jpeg\" alt=\"\" class=\"wp-image-250343\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A 78-rpm record turns at the rate of 78 revolutions per minute, as its name implies. Through what angle (in radians) would such a record turn during a song that lasted for 3 minutes and 15 seconds? The Correct Answer and Explanation is: To solve this problem, we need to determine how many radians the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-250339","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250339","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=250339"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250339\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}