{"id":23680,"date":"2021-10-03T20:26:50","date_gmt":"2021-10-03T14:56:50","guid":{"rendered":"https:\/\/python-programs.com\/?p=23680"},"modified":"2021-11-22T18:33:26","modified_gmt":"2021-11-22T13:03:26","slug":"python-program-for-volume-and-surface-area-of-frustum-of-cone","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-for-volume-and-surface-area-of-frustum-of-cone\/","title":{"rendered":"Python Program for Volume and Surface Area of Frustum of Cone"},"content":{"rendered":"<p>Given the height, slant height, smaller and bigger radius of a frustum cone, the task is to find the volume and surface area of the frustum of a given cone in python.<\/p>\n<p><strong>Frustum of a Cone :<\/strong><\/p>\n<p>A frustum in geometry is the portion of a solid (typically a cone or pyramid) that lies between one or two parallel planes that cut it.<br \/>\nThe portion of a solid between a plane parallel to the base and a right circular cone is known as the frustum of a cone.<\/p>\n<p>A right circular cone is shown below:<\/p>\n<p>After being cut by a plane parallel to its base, the right circular cone produces the following frustum:<\/p>\n<p>which has a circular base with radius R at the bottom, a circular upper portion with radius R height h, and a slant height l.<\/p>\n<blockquote><p><strong>Formulas:<\/strong><\/p>\n<p>volume of the frustum of a cone = 1\/3 * pi * h(r<sup>2<\/sup> + R<sup>2<\/sup> + r*R)<\/p>\n<p>The curved surface area of a frustum of a cone = pi * l(R+r)<\/p>\n<p>The total surface area of a frustum of a cone = pi * l(R+r) + pi(R<sup>2<\/sup> + r<sup>2<\/sup>)<\/p>\n<p>In which,<\/p>\n<p><strong>r<\/strong> is the radius of the smaller circle<\/p>\n<p><strong>R<\/strong> is the radius of the bigger circle<\/p>\n<p><strong>l<\/strong> is the slant height of the frustum of a cone.<\/p><\/blockquote>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given smaller radius = 3\r\nGiven bigger radius = 6\r\nGiven slant height = 8\r\nGiven height  = 10<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Volume of above given Frustum of Cone =  659.7344572538565\r\nThe curved surface area of the above given frustum of Cone =  226.1946710584651\r\nThe total surface area of the above given frustum of Cone :  367.5663404700058<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given smaller radius = 4\r\nGiven bigger radius = 7\r\nGiven slant height = 10\r\nGiven height = 15<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>The Volume of above given Frustum of Cone = 1460.8405839192537\r\nThe curved surface area of the above given frustum of Cone = 345.57519189487726\r\nThe total surface area of the above given frustum of Cone : 549.7787143782139<\/pre>\n<h2>Program for Volume and Surface Area of Frustum of Cone in Python<\/h2>\n<p>Below are the ways to find the volume and surface area of the frustum of a given cone in python:<\/p>\n<ul>\n<li><a href=\"#Using_Mathematical_Formula_(Static_Input)\">Using Mathematical Formula (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Mathematical_Formula_(User_Input)\">Using Mathematical Formula (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Mathematical_Formula_(Static_Input)\">Method #1: Using Mathematical Formula (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Get the value of pi using the math.pi function and store it in a variable.<\/li>\n<li>Give the radius of the smaller circle as static input and store it in a variable.<\/li>\n<li>Give the radius of the bigger circle as static input and store it in another variable.<\/li>\n<li>Give the slant height of the frustum cone as static input and store it in another variable.<\/li>\n<li>Give the height as static input and store it in another variable.<\/li>\n<li>Calculate the volume of the frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Calculate the curved surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Calculate the total surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Print the volume of the frustum of a cone.<\/li>\n<li>Print the curved surface area of a frustum of a cone.<\/li>\n<li>Print the Total surface area of a frustum of a cone.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Import math module using the import keyword.\r\nimport math\r\n# Get the value of pi using the math.pi function and store it in a variable.\r\npi_val = math.pi\r\n# Give the radius of the smaller circle as static input and store it in a variable.\r\ngvn_smallrradiuss = 3\r\n# Give the radius of the bigger circle as static input and store it in another variable.\r\ngvn_biggradiuss = 6\r\n# Give the slant height of the frustum cone as static input and store it in\r\n# another variable.\r\ngvn_slantheigt = 8\r\n# Give the height as static input and store it in another variable.\r\ngvn_heigt = 10\r\n# Calculate the volume of the frustum of a cone using the above given mathematical\r\n# formula and store it in another variable.\r\nrslt_vol = 1 \/ 3 * pi_val * gvn_heigt * \\\r\n    (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss *\r\n     gvn_biggradiuss + gvn_smallrradiuss * gvn_biggradiuss)\r\n# Calculate the curved surface area of a frustum of a cone using the above given\r\n# mathematical formula and store it in another variable.\r\ncurvd_surfce_area = pi_val * gvn_slantheigt * \\\r\n    (gvn_biggradiuss + gvn_smallrradiuss)\r\n# Calculate the total surface area of a frustum of a cone using the above given\r\n# mathematical formula and store it in another variable.\r\ntotl_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss) + pi_val * \\\r\n    (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss)\r\n# Print the volume of the frustum of a cone.\r\nprint(\"The Volume of above given Frustum of Cone = \", rslt_vol)\r\n# Print the curved surface area of a frustum of a cone.\r\nprint(\"The curved surface area of the above given frustum of Cone = \", curvd_surfce_area)\r\n# Print the Total surface area of a frustum of a cone.\r\nprint(\"The total surface area of the above given frustum of Cone : \", totl_surfce_area)\r\n<\/pre>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">#include &lt;cmath&gt;\r\n#include &lt;iostream&gt;\r\n\r\nusing namespace std;\r\n\r\nint main()\r\n{\r\n    int argc = 2;\r\n    double pi_val = M_PI;\r\n    double gvn_smallrradiuss = 3;\r\n    int gvn_biggradiuss = 6;\r\n    int gvn_slantheigt = 8;\r\n    int gvn_heigt = 10;\r\n    double rslt_vol\r\n        = 1 \/ 3 * pi_val * gvn_heigt\r\n          * (gvn_smallrradiuss * gvn_smallrradiuss\r\n             + gvn_biggradiuss * gvn_biggradiuss\r\n             + gvn_smallrradiuss * gvn_biggradiuss);\r\n    double curvd_surfce_area\r\n        = pi_val * gvn_slantheigt\r\n          * (gvn_biggradiuss + gvn_smallrradiuss);\r\n    double totl_surfce_area\r\n        = pi_val * gvn_slantheigt\r\n              * (gvn_biggradiuss + gvn_smallrradiuss)\r\n          + pi_val * gvn_smallrradiuss * gvn_smallrradiuss\r\n          + gvn_biggradiuss * gvn_biggradiuss;\r\n    \/\/ Print the volume of the frustum of a cone.\r\n    cout &lt;&lt; \"The Volume of above given Frustum of Cone = \"\r\n         &lt;&lt; rslt_vol &lt;&lt; endl;\r\n    \/\/ Print the curved surface area of a frustum of a cone.\r\n    cout &lt;&lt; \"The curved surface area of the above given \"\r\n            \"frustum of Cone = \"\r\n         &lt;&lt; curvd_surfce_area &lt;&lt; endl;\r\n    \/\/ Print the Total surface area of a frustum of a cone.\r\n    cout &lt;&lt; \"The total surface area of the above given \"\r\n            \"frustum of Cone :\"\r\n         &lt;&lt; totl_surfce_area;\r\n}<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The Volume of above given Frustum of Cone =  659.7344572538565\r\nThe curved surface area of the above given frustum of Cone =  226.1946710584651\r\nThe total surface area of the above given frustum of Cone :  367.5663404700058<\/pre>\n<h3 id=\"Using_Mathematical_Formula_(User_Input)\">Method #2: Using Mathematical Formula (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Get the value of pi using the math.pi function and store it in a variable.<\/li>\n<li>Give the radius of the smaller circle as user input using the float(input()) function and store it in a variable.<\/li>\n<li>Give the radius of the bigger circle as user input using the float(input()) function and store it in another variable.<\/li>\n<li>Give the slant height of the frustum cone as user input using the float(input()) function and store it in another variable.<\/li>\n<li>Give the height as user input using the float(input()) function and store it in another variable.<\/li>\n<li>Calculate the volume of the frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Calculate the curved surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Calculate the total surface area of a frustum of a cone using the above given mathematical formula and store it in another variable.<\/li>\n<li>Print the volume of the frustum of a cone.<\/li>\n<li>Print the curved surface area of a frustum of a cone.<\/li>\n<li>Print the Total surface area of a frustum of a cone.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Import math module using the import keyword.\r\nimport math\r\n# Get the value of pi using the math.pi function and store it in a variable.\r\npi_val = math.pi\r\n# Give the radius of the smaller circle as user input using the float(input()) function\r\n# and store it in a variable.\r\ngvn_smallrradiuss = float(input(\"Enter some random number = \"))\r\n# Give the radius of the bigger circle as user input using the float(input()) function \r\n# and store it in another variable.\r\ngvn_biggradiuss = float(input(\"Enter some random number = \"))\r\n# Give the slant height of the frustum cone as user input using the float(input()) function\r\n# and store it in another variable.\r\ngvn_slantheigt = float(input(\"Enter some random number = \"))\r\n# Give the height as user input using the float(input()) function and\r\n# store it in another variable.\r\ngvn_heigt = float(input(\"Enter some random number = \"))\r\n# Calculate the volume of the frustum of a cone using the above given mathematical\r\n# formula and store it in another variable.\r\nrslt_vol = 1 \/ 3 * pi_val * gvn_heigt * \\\r\n    (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss *\r\n     gvn_biggradiuss + gvn_smallrradiuss * gvn_biggradiuss)\r\n# Calculate the curved surface area of a frustum of a cone using the above given\r\n# mathematical formula and store it in another variable.\r\ncurvd_surfce_area = pi_val * gvn_slantheigt * \\\r\n    (gvn_biggradiuss + gvn_smallrradiuss)\r\n# Calculate the total surface area of a frustum of a cone using the above given\r\n# mathematical formula and store it in another variable.\r\ntotl_surfce_area = pi_val * gvn_slantheigt * (gvn_biggradiuss + gvn_smallrradiuss) + pi_val * \\\r\n    (gvn_smallrradiuss * gvn_smallrradiuss + gvn_biggradiuss * gvn_biggradiuss)\r\n# Print the volume of the frustum of a cone.\r\nprint(\"The Volume of above given Frustum of Cone = \", rslt_vol)\r\n# Print the curved surface area of a frustum of a cone.\r\nprint(\"The curved surface area of the above given frustum of Cone = \", curvd_surfce_area)\r\n# Print the Total surface area of a frustum of a cone.\r\nprint(\"The total surface area of the above given frustum of Cone : \", totl_surfce_area)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 4\r\nEnter some random number = 7\r\nEnter some random number = 10\r\nEnter some random number = 15\r\nThe Volume of above given Frustum of Cone = 1460.8405839192537\r\nThe curved surface area of the above given frustum of Cone = 345.57519189487726\r\nThe total surface area of the above given frustum of Cone : 549.7787143782139<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given the height, slant height, smaller and bigger radius of a frustum cone, the task is to find the volume and surface area of the frustum of a given cone in python. 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