The volume of a right circular cone with height h and base radius r.
Use the definition of Volume
2) Definition of volume:
Let S be a solid that lies between x=a and x=b. If the cross sectional area of S in the plane Px, through x and perpendicular to the x-axis, is A(x), where A is continuous function, then the volume of S is
Cone with height h, and base radius r.
Consider the cone positioned about x-axis, as shown in the diagram.
At x, a slice through the cone (cross section) is circular disk. Let it’s radius be R.
By property of similar triangles,
Hence, the area of that cross sectional slice is
Integrating this function from 0 to h will yield the volume of the required cone
By the fundamental theorem of Calculus,
The volume of a right circular cone with height h and base radius r is πr2h3