{"id":1044,"date":"2018-12-30T20:21:54","date_gmt":"2018-12-30T19:21:54","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=1044"},"modified":"2024-02-16T10:17:37","modified_gmt":"2024-02-16T09:17:37","slug":"how-to-calculate-and-solve-for-the-area-radius-diameter-and-angle-of-a-sector-the-calculator-encyclopedia","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2018\/12\/30\/how-to-calculate-and-solve-for-the-area-radius-diameter-and-angle-of-a-sector-the-calculator-encyclopedia\/","title":{"rendered":"How to Calculate and Solve for the Area, Radius, Diameter and Angle of a Sector | The Calculator Encyclopedia"},"content":{"rendered":"

\"\"<\/p>\n

The image above is a sector. To calculate the area of a sector, two essential parameters is needed and this parameters are the radius of the sector (r) and the angle of the sector (\u03b8). You can also use the diameter of the sector (d).<\/p>\n

The formula for calculating the area of a sector:<\/p>\n

Area of a sector = (\u03b8\/360)[\u03c0r\u00b2]<\/p>\n

Where;<\/p>\n

A<\/b>\u00a0= Area of the Sector
\nr = Radius of the Sector
\n\u03b8 = Angle of the Sector<\/p>\n

Let\u2019s solve an example:
\nFind the area of a sector when the radius of the sector is 7 cm and the angle of the sector is 9\u00b0<\/p>\n

This implies that;<\/p>\n

r = Radius of the sector = 7 cm
\n\u03b8 = Angle of the sector = 9\u00b0<\/p>\n

A = \u03b8 \/ 360<\/sub> x \u03c0r2<\/sup>
\nA = (9\/360)[\u03c0 x 7\u00b2]
\nSo, A = 0.025 x \u03c0 x 49
\nA = 3.848<\/p>\n

Therefore, the area of the sector<\/strong> is 3.848 cm2.<\/sup><\/strong><\/p>\n

Calculating the Area of a Sector using Diameter and Angle of the sector.<\/strong><\/h3>\n

The formula is A = \u03b8 \/ 360<\/sub> x \u03c0d2<\/sup> \/ 4<\/sub><\/p>\n

Where;<\/p>\n

\u03b8 = Angle of the sector
\nd = Diameter of the sector<\/p>\n

Let’s solve an example;
\nFind the Area of a sector when the diameter of the sector is 12 cm and the angle of the sector is 18\u00b0.<\/p>\n

This implies that;<\/p>\n

d = Diameter of the sector = 12 cm
\n\u03b8 = Angle of the sector = 18\u00b0<\/p>\n

A = \u03b8 \/ 360<\/sub> x \u03c0d2<\/sup> \/ 4<\/sub>
\nA = 18 \/ 360<\/sub> x 3.142 (144) \/ 4<\/sub>
\nSo, A = 18 \/ 360<\/sub> x 452.448 \/ 4<\/sub>
\nA=\u00a018 \/ 360<\/sub> x\u00a0113.112
\nA=\u00a00.05 x 113.112
\nThen, A = 5.656<\/p>\n

Therefore, the area of the sector<\/strong> with diameter is 5.656 cm2\u00a0<\/sup><\/strong><\/p>\n

How to Calculate Angle of a Sector when Area of the Sector and Radius of the Sector is Given<\/strong><\/h3>\n

\u03b8 = 360 (A)<\/sup> \/ \u03c0r2<\/sup><\/sub><\/p>\n

where;<\/p>\n

r = Radius of a sector
\nA = Area of a sector<\/p>\n

Let’s solve an example;
\nGiven that the area of a sector is 15 cm2<\/sup> and the radius of the sector is 5 cm. Find the angle of the sector?<\/p>\n

This implies that;
\nA = Area of the sector =\u00a015 cm2<\/sup>
\nr = Radius of the sector = 5 cm<\/p>\n

\u03b8 = 360 (A)<\/sup> \/ \u03c0r2<\/sup><\/sub>
\n\u03b8 = 360 (15)<\/sup> \/ 3.142 (5)2<\/sup><\/sub>
\nThat is, \u03b8 = 5400<\/sup> \/ 3.142 (25)<\/sub>
\n\u03b8 = 5400<\/sup> \/ 78.55<\/sub>
\n\u03b8 = 68.746<\/p>\n

Therefore, the angle of the sector<\/strong> is 68.746\u00b0.<\/strong><\/p>\n

How to Calculate Angle of a Sector when Area of the Sector and Diameter of the Sector is Given<\/strong><\/h3>\n

\u03b8 = 1440 (A)<\/sup> \/ \u03c0d2<\/sup><\/sub><\/p>\n

where;<\/p>\n

d = Diameter of a sector
\nA = Area of a sector<\/p>\n

Let’s solve an example;
\nGiven that the area of a sector is 22 cm2<\/sup> and the diameter of the sector is 10 cm. Find the angle of the sector?<\/p>\n

This implies that;
\nA = Area of the sector = 22 cm2<\/sup>
\nd = Diameter of the sector = 10 cm<\/p>\n

\u03b8 = 1440 (A)<\/sup> \/ \u03c0r2<\/sup><\/sub>
\n\u03b8 = 1440 (22)<\/sup> \/ 3.142 (10)2<\/sup><\/sub>
\nThen, \u03b8 = 31680<\/sup> \/ 3.142 (100)<\/sub>
\n\u03b8 = 31680<\/sup> \/ 314.2<\/sub>
\n\u03b8 = 100.88<\/p>\n

Therefore, the angle of the sector<\/strong> is 100.88\u00b0.<\/strong><\/p>\n

How to Calculate Diameter of a Sector when Area of the Sector and Angle of the Sector is Given<\/strong><\/h3>\n

d = \u221a1440 (A)<\/sup> \/ \u03c0\u03b8<\/sub><\/p>\n

where;<\/p>\n

\u03b8\u00a0= Angle of a sector
\nA = Area of a sector<\/p>\n

Let’s solve an example;
\nGiven that the area of a sector is 24 cm2<\/sup> and the angle of the sector is 10\u00b0<\/strong>. Find the diameter of the sector?<\/p>\n

This implies that;
\nA = Area of the sector = 24 cm2<\/sup>
\n\u03b8\u00a0= Angle of the sector = 10\u00b0<\/strong><\/p>\n

d = \u221a1440 (A)<\/sup> \/ \u03c0\u03b8<\/sub>
\nd = \u221a1440 (24)<\/sup> \/ 3.142 x 10<\/sub>
\nSo, d = \u221a34560<\/sup> \/ 31.42<\/sub>
\nd = \u221a1099.936
\nd = 33.165<\/p>\n

Therefore, the diameter of the sector<\/strong> is 33.165 cm.<\/strong><\/p>\n

How to Calculate Radius of a Sector when Area of the Sector and Angle of the Sector is Given<\/strong><\/h3>\n

r = \u221a360 (A)<\/sup> \/ \u03c0\u03b8<\/sub><\/p>\n

where;<\/p>\n

\u03b8\u00a0= Angle of a sector
\nA = Area of a sector<\/p>\n

<\/p>\n

Let’s solve an example;
\nGiven that the area of a sector is 30 cm2<\/sup> and the angle of the sector is 20\u00b0<\/strong>. Find the radius of the sector?<\/p>\n

This implies that;
\nA = Area of the sector = 30 cm2<\/sup>
\n\u03b8\u00a0= Angle of the sector = 20\u00b0<\/strong><\/p>\n

So, we have r = \u221a360 (A)<\/sup> \/ \u03c0\u03b8<\/sub><\/p>\n

r = \u221a360 (30)<\/sup> \/ \u03c020<\/sub>
\nr = \u221a10800<\/sup> \/ 3.142 x 20<\/sub>
\nThat is, r = \u221a10800<\/sup> \/ 62.84<\/sub>
\nr = \u221a171.865
\nr = 13.11<\/p>\n

Therefore. the radius of the sector<\/strong> is 13.11 cm.<\/strong><\/p>\n

How to Calculate and Solve for the Area of a Sector Using Nickzom Calculator<\/strong><\/h3>\n

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

To get the answer and workings of the area of a sector 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\u00a0Area of a Sector<\/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 area of a sector according to the respective parameters which are the radius of the sector (r) and angle of the sector (\u03b8).<\/p>\n

\"How<\/p>\n

Now, enter the value appropriately and accordingly for the parameters as required by the\u00a0example<\/strong>\u00a0above where the\u00a0radius of the sector<\/strong>\u00a0is\u00a07 cm<\/strong> and angle of the sector<\/strong> is 9\u00b0.<\/strong><\/p>\n

\"\"<\/p>\n

Finally, click on\u00a0Calculate<\/strong><\/p>\n

\"\"<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u00a0\u2013 The Calculator Encyclopedia solves for the area of a sector and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above is a sector. To calculate the area of a sector, two essential parameters is needed…","protected":false},"author":5,"featured_media":12507,"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":"","_members_access_role":[],"_members_access_error":""},"categories":[4],"tags":[385,246,386,84,323,387,56,349,87,326,312],"class_list":["post-1044","post","type-post","status-publish","format-standard","has-post-thumbnail","category-mathematics","tag-angle","tag-area","tag-area-of-a-sector","tag-calculator-encyclopedia","tag-diameter","tag-diameter-of-a-sector","tag-mathematics","tag-mensuration","tag-nickzom-calculator","tag-radius","tag-radius-of-a-sector","cs-entry"],"yoast_head":"\nHow 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