Volume of Cone
- The cone is the three-dimensional geometrical figure or object which has the base in the form of circle of some radius. It also has height and slant height.
- And the right circular cone is that cone which is perpendicular to the circular base of the cone.
- The space occupied by the cone is called as the volume of the cone.
- Following figure shows the cone with base radius r, slant height l and height h.
Derivation for Volume of Cone:
- Let us consider the cone of base radius r, slant height l and height h as shown in figure.
- Now take a cylinder of known volume πr2h whose base radius is also r, height h.
- We see here that; the base radius and height of the cylinder and cone are same.
- To find the volume of cone we use the volume of cylinder formula.
- Now, if have filled the cone with water and poured it into cylinder then to fill the complete cylinder it requires three completely filled cones.
- Hence, we can say that the volume of cylinder is 3 times the volume of cone.
Thus, we can write as
Volume of cylinder of height h and base radius r = 3* volume of cone of base radius r and height h
- But we already know that
the volume of cylinder = πr2h
Thus,
πr2h = 3* volume of cone
Hence, volume of cone = 1/3* πr2h (Hence proved.