{"id":1301,"date":"2019-01-10T15:49:41","date_gmt":"2019-01-10T14:49:41","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=1301"},"modified":"2024-02-17T16:26:00","modified_gmt":"2024-02-17T15:26:00","slug":"how-to-calculate-and-solve-for-the-total-surface-area-of-a-conical-frustum-the-calculator-encyclopedia","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/01\/10\/how-to-calculate-and-solve-for-the-total-surface-area-of-a-conical-frustum-the-calculator-encyclopedia\/","title":{"rendered":"How to Calculate and Solve for the Total Surface Area of a Conical Frustum | The Calculator Encyclopedia"},"content":{"rendered":"

\"\"<\/p>\n

The image above is a conical frustum. To calculate the total surface area of a conical frustum requires three essential parameters which are the radius of the lower base (R), the radius of the upper base (r), and the height (h).<\/p>\n

The formula for calculating the total surface area of a conical frustum;<\/p>\n

A = \u03c0[R\u00b2 + r\u00b2 + (R + r)\u221a((R – r)\u00b2 + h\u00b2)]<\/p>\n

Where;
\nA = Total surface area of the conical frustum
\nR = Radius of the lower base
\nr = Radius of the upper base
\nh = Height of the conical frustum<\/p>\n

Let’s solve an example;
\nFind the total surface area of the conical frustum when the radius of the upper base is 11 cm, radius of the lower base is 17 cm and the height is 30 cm.<\/p>\n

This implies that;
\nr = Radius of the upper base = 11 cm
\nR = Radius of the lower base = 17 cm
\nh = Height of the conical frustum = 30 cm<\/p>\n

A = \u03c0[R\u00b2 + r\u00b2 + (R + r)\u221a((R – r)\u00b2 + h\u00b2)]
\nA = \u03c0[17\u00b2 + 11\u00b2 + (17 + 11)\u221a((17 – 11)\u00b2 + 30\u00b2)]
\nSo, A = \u03c0[289 + 121 + (28)\u221a((6)\u00b2 + 900)]
\nA = \u03c0[289 + 121 + (28)\u221a(36+ 900)]
\nA = \u03c0[289 + 121 + (28)\u221a(936)]
\nThen, A = \u03c0[289 + 121 + (28)(30.59)]
\nA = \u03c0[289 + 121 + 856.63]
\nA = \u03c0[1266.63]
\nThat is, A = 3979.25<\/p>\n

Therefore, the total surface area of the conical frustum<\/strong> is 3979.25 cm\u00b2.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for the Lateral Surface Area of a Conical Frustum | Nickzom Calculator<\/a><\/p>\n

How to Calculate the Total Surface Area of a Conical Frustum Using Nickzom Calculator<\/strong><\/h3>\n

<\/p>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong>\u00a0is capable of calculating the total surface area of a conical frustum.<\/p>\n

To get the answer and workings of the total surface area of a conical frustum using the\u00a0Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><\/p>\n

Once, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Mensuration<\/strong>\u00a0<\/strong>under the\u00a0Mathematics<\/strong>\u00a0section.<\/p>\n

\"How<\/p>\n

Now, click on Total\u00a0Surface area of a conical frustum<\/strong>\u00a0under\u00a0Mensuration<\/strong><\/p>\n

\"How<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the total surface area of a conical frustum according to the respective parameters which are the radius of the lower base (R), radius of the lower base (r) and the height of the conical frustum.<\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the\u00a0example<\/strong>\u00a0above where the\u00a0radius of the lower base\u00a0<\/strong>is\u00a017 cm<\/strong>,\u00a0radius of the upper base\u00a0<\/strong>is\u00a011 cm<\/strong>\u00a0and\u00a0the height<\/strong>\u00a0is\u00a030 cm.<\/strong><\/p>\n

\"\"<\/p>\n

Finally, Click on Calculate<\/p>\n

\"\"<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u00a0\u2013 The Calculator Encyclopedia solves for the\u00a0Total Surface area of a conical frustum<\/strong>\u00a0and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above is a conical frustum. To calculate the total surface area of a conical frustum requires…","protected":false},"author":5,"featured_media":12632,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Total Surface Area Conical Frustum","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Here's a complete guide on How to Calculate and Solve for the Total Surface Area of a Conical Frustum | The Calculator Encyclopedia","_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[4],"tags":[84,446,451,318,56,349,87,326,450,452],"class_list":["post-1301","post","type-post","status-publish","format-standard","has-post-thumbnail","category-mathematics","tag-calculator-encyclopedia","tag-conical-frustum","tag-frustum","tag-height","tag-mathematics","tag-mensuration","tag-nickzom-calculator","tag-radius","tag-total-surface-area","tag-total-surface-area-of-a-conical-frustum","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for the Total Surface Area of a Conical Frustum | The Calculator Encyclopedia<\/title>\n<meta name=\"description\" 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