A frustum may be formed from a cone with a circular base by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and an upper base that are circular and parallel.
Let h be the height, R the radius of the lower base, and r the radius of the upper base. One picture of the frustum is the following.
Given R, r, and h, find the volume of the frustum.
The Formula
Extensions:
1. Derive the formula.
2. What is the area of the curved surface of the frustum of a right circular cone? what is the total surface area of the frustum?
3. What is the volume of a frustum formed from square based pyramid of height h, lower base having a side length of S, and an upper base of side length s?
Note: See Polya, G. (1965) Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, Volume II, Chapter 7, pp. 1-21, for discussions of finding the volume of a square based frustum.
4. What is the total surface area of the square based frustum?
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