Frustum of a Right Circular Cone Formula
Frustum of a right circular cone is that portion of right circular cone included between the base and a section parallel to the base not passing through the vertex.
Properties of Frustum of Right Circular Cone
- The altitude of a frustum of a right circular cone is the perpendicular distance between the two bases. It is denoted by h.
- All elements of a frustum of a right circular cone are similar to a cone. Here, slant height is denoted by L.
| The formula of Frustum of a Right Circular Cone
CSA = πL(R + r) TSA = πL(R + r) + πR2+ πr2 V0lume, V = \(\begin{array}{l}\frac{\pi h}{3} \left ( R^{2}+ Rr + r^{2} \right)\end{array} \) |
Solved Example
Question:Â Find the volume of a frustum of a right circular cone with height 20, lower base radius 34 and top radius 19.
Solution:
Given,
h = 20
R = 34
r = 19
V =
\(\begin{array}{l}\frac{\pi h}{3} \left ( R^{2}+ Rr + r^{2} \right)\end{array} \)
V =
\(\begin{array}{l}\frac{\pi \times 20}{3} \left (34^{2} + 34 \times 19 + 19^{2} \right)\end{array} \)
V = 14420 π cubic units
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