Consider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H h'. There are two formulas that are used to calculate the volume of a frustum of a cone. When your measurement is uploaded and processed you will see that it is in a Ready for approval state. You won’t consume that measurement until you tap the Accept measurement button. V = πH/3 (R 2 Rr r 2) What Is the Volume of the Frustum of a Cone Formula? The Stockpile Reports Lite App enables you to re-measure a pile as many times as you like. We can use this formula to calculate one of the unknown values among 'r', 'R', and 'H' and then we can find the volume (V) of the frustum using the formula: The relation between the height (H), slant height (L), and base radii R and r of the frustum of the cone is, L 2 = H 2 (R - r) 2. What Is the Volume of the Frustum of a Cone Formula Using Slant Height?Ĭonsider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H h'. \(S_2\) = The area of the other base square of the frustum.\(S_1\) = The area of the one base square of the frustum.Substituting these values in the volume of frustum formula, The base areas ( areas of circles) of the frustum of the cone from the above figure are: We will use the volume of frustum formula (from the previous section) to derive the volume of the frustum of a circular cone. Method 1 to Derive the Volume of Frustum of Cone Formula Note: Here π is a constant whose value is 22/7 (or) 3.141592653. Volume measurement using the traditional method: (a) stockpile carried on a barge (b) manual operation for reshaping the surface of the stockpile (c) stockpile with a trapezoidal surface. Volume of frustum of cone = πH/3 (R 2 Rr r 2) Then the volume of the frustum of the cone is, Here, L and L l are the slant heights of the frustum and the cone respectively. Also, consider the frustum of a cone of height H with a small base radius 'r' and the large base radius 'R'. In both the methods, consider a cone of height H h and base radius R. While solving the problems in geometry, we usually come across with frustum of a cone and here we will see how to derive the formula of the volume of a frustum of a cone. The formula which we learned in the previous section can be used to calculate the volume of any frustum and hence it can be used to calculate the volume of the frustum of a cone as well.
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