{"id":1317,"date":"2019-01-11T00:12:07","date_gmt":"2019-01-10T23:12:07","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=1317"},"modified":"2024-02-17T17:24:28","modified_gmt":"2024-02-17T16:24:28","slug":"how-to-calculate-the-radius-height-and-curved-surface-area-of-a-spherical-cap-the-calculator-encyclopedia","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/01\/11\/how-to-calculate-the-radius-height-and-curved-surface-area-of-a-spherical-cap-the-calculator-encyclopedia\/","title":{"rendered":"How to Calculate the Radius, Height and Curved Surface Area of a Spherical Cap | The Calculator Encyclopedia"},"content":{"rendered":"

\"\"<\/p>\n

The image above is a spherical cap. To calculate the curved surface area of a spherical cap requires two essential parameters which are the radius of the base of the cap (a) and the height (h).<\/p>\n

The formula for calculating the curved surface area of the spherical cap:<\/p>\n

A = \u03c0(a\u00b2 + h\u00b2)<\/p>\n

Where;
\nA = Curved surface area of the spherical cap
\na = Radius of the base of the cap
\nh = Height of the spherical cap<\/p>\n

Let’s solve an example;
\nFind the curved surface area of a spherical cap with radius of the base 7 cm and the height of 13 cm.<\/p>\n

This implies that;
\na = Radius of the base of the cap = 7 cm
\nh = Height of the spherical cap = 13 cm<\/p>\n

A = \u03c0(a\u00b2 + h\u00b2)
\nA =\u00a0 \u03c0(7\u00b2 + 13\u00b2)
\nThen, A =\u00a0 \u03c0(49 + 169)
\nA =\u00a0 \u03c0(218)
\nA = 684.867<\/p>\n

Therefore, the curved surface area of the spherical cap<\/strong> is 684.867 cm\u00b2.<\/strong><\/p>\n

Calculating the Radius of the base of a Spherical Cap using the Curved Surface Area of the Spherical Cap and the Height<\/strong><\/h3>\n

a = \u221aA – \u03c0h2<\/sup><\/sup> \/ \u03c0<\/sub><\/p>\n

Where;
\nA = Curved surface area of the spherical cap
\na = Radius of the base of the cap
\nh = Height of the spherical cap<\/p>\n

Let’s solve an example;
\nFind the radius of the base of a spherical cap when the curved surface area of the spherical cap is 300 cm2<\/sup> and a height of 7 cm.<\/p>\n

This implies that;
\nA = Curved surface area of the spherical cap = 300\u00a0cm2<\/sup>
\nh = Height of the spherical cap = 7 cm<\/p>\n

a = \u221aA – \u03c0h2<\/sup><\/sup> \/ \u03c0<\/sub>
\na = \u221a300 – 3.142 x 72<\/sup><\/sup> \/ \u03c0<\/sub>
\nSo, a = \u221a300 – 3.142 x 49<\/sup> \/ \u03c0<\/sub>
\na = \u221a300 – 153.958<\/sup> \/ \u03c0<\/sub>
\na = \u221a146.042<\/sup> \/ \u03c0<\/sub>
\nThat is, a = \u221a46.48
\na = 6.82<\/p>\n

Therefore, the radius of the base of the cap<\/strong> is 6.82 cm.<\/strong><\/p>\n

<\/p>\n

Calculating the Height of a Spherical Cap using the Curved Surface Area of the Spherical Cap and the Radius of the base of the Cap<\/strong><\/h3>\n

h = \u221aA – \u03c0a2<\/sup><\/sup> \/ \u03c0<\/sub><\/p>\n

Where;
\nA = Curved surface area of the spherical cap
\na = Radius of the base of the cap
\nh = Height of the spherical cap<\/p>\n

Let’s solve an example;
\nFind the height of a spherical cap when the curved surface area of the spherical cap is 420 cm2<\/sup> and the radius of the base of the cap is 9 cm.<\/p>\n

This implies that;
\nA = Curved surface area of the spherical cap = 420\u00a0cm2<\/sup>
\nr = Radius of the base of the spherical cap = 9 cm<\/p>\n

h = \u221aA – \u03c0a2<\/sup><\/sup> \/ \u03c0<\/sub>
\nh = \u221a420 – 3.142 x 92<\/sup><\/sup> \/ \u03c0<\/sub>
\nThat is, h = \u221a420 – 3.142 x 81<\/sup> \/ \u03c0<\/sub>
\nh = \u221a420 – 254.502<\/sup> \/ \u03c0<\/sub>
\nh = \u221a165.498<\/sup> \/ \u03c0<\/sub>
\nThen, h = \u221a52.67
\nh = 7.26<\/p>\n

Therefore, the height of the spherical cap<\/strong> is 7.26 cm.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for the Volume of a Spherical Cap | Nickzom Calculator<\/a><\/p>\n

How to Calculate the Curved Surface Area of a Spherical Cap Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong>\u00a0is capable of calculating the curved surface area of the spherical cap.<\/p>\n

To get the answer and workings of the curved surface area of the spherical cap 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 Curved Surface Area\u00a0of the spherical cap<\/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 curved surface area of the spherical cap according to the respective parameters which are the radius of the base of the cap (a) and height (h).<\/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 base of the cap\u00a0<\/strong>is 7 cm\u00a0<\/strong>and\u00a0the height\u00a0<\/strong>is 13\u00a0cm.<\/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\u00a0Curved Surface Area of a spherical cap<\/strong>\u00a0and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above is a spherical cap. To calculate the curved surface area of a spherical cap requires…","protected":false},"author":5,"featured_media":12639,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_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":[84,455,456,318,56,349,87,326,457,454],"class_list":["post-1317","post","type-post","status-publish","format-standard","has-post-thumbnail","category-mathematics","tag-calculator-encyclopedia","tag-curved-surface-area","tag-curved-surface-area-of-a-spherical-cap","tag-height","tag-mathematics","tag-mensuration","tag-nickzom-calculator","tag-radius","tag-radius-of-the-base-of-a-cap","tag-spherical-cap","cs-entry"],"yoast_head":"\nHow 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