{"id":10232,"date":"2022-02-27T23:02:51","date_gmt":"2022-02-27T17:32:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10232"},"modified":"2022-03-01T00:00:44","modified_gmt":"2022-02-28T18:30:44","slug":"volume-of-a-frustum-of-a-cone-formula-and-derivation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/volume-of-a-frustum-of-a-cone-formula-and-derivation\/","title":{"rendered":"Volume of a Frustum of a Cone – Formula and Derivation"},"content":{"rendered":"
Here you will learn formula for the volume of a frustum of a cone with derivation and examples based on it.<\/p>\n
Let’s begin –\u00a0<\/p>\n
What is Frustum of Cone ?<\/h2>\n
Frustum of a cone<\/strong> is the solid obtained after removing the upper portion of the cone by a plane parallel to its base. The lower portion is the frustum of a cone.<\/p>\n
Height<\/strong> : The perpendicular distance between the aforesaid plane and the base is called the height of the frustum.<\/p>\n
Volume of a Frustum of a Cone<\/h2>\n
The formula for volume of a frustum of a cone is<\/p>\n
\n
V = \\(h\\over 3\\)\\([A_1 + \\sqrt{A_1A_2} + A_2]\\)<\/p>\n<\/blockquote>\n
[\\(A_1\\), \\(A_2\\) are the areas of bottom and top of the frustum]<\/p>\n
\n
V = \\(\\pi h\\over 3\\)\\([{r_1}^2 + \\sqrt{r_1r_2} + {r_2}^2]\\)<\/p>\n<\/blockquote>\n
where h is the height of the frustum, \\(r_1\\), \\(r_2\\) are the radii of the base and the top of frustum of a cone.<\/p>\n
Note<\/strong> : Height h of the frustum is given by the relation,<\/p>\n