Frustum

Definition

A frustum is the portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it. It can be generated by slicing the solid with a plane parallel to its base and removing the top portion.

5 Must Know Facts For Your Next Test

1. A frustum of a cone or pyramid has two bases: one larger, one smaller.
2. The volume of a frustum can be calculated using the formula $V = \frac{1}{3}h(A_1 + A_2 + \sqrt{A_1 A_2})$, where $h$ is the height and $A_1$, $A_2$ are the areas of the bases.
3. The lateral surface area of a conical frustum is given by $\pi(r_1 + r_2)l$, where $r_1$ and $r_2$ are the radii of the bases and $l$ is the slant height.
4. In calculus, frustums are often used in integration problems to find volumes and surface areas by rotating curves around an axis.
5. The concept of a frustum is essential for understanding approximations in integral calculus, especially when dealing with solids of revolution.

Review Questions

• What is the formula for calculating the volume of a frustum?
• How do you determine the lateral surface area of a conical frustum?
• What role does a frustum play in integral calculus when finding volumes of solids?

Related terms

Solid of Revolution: A three-dimensional object obtained by rotating a two-dimensional shape around an axis.

Lateral Surface Area: The area of all sides of a three-dimensional object excluding its base and top surfaces.

Integration: A fundamental concept in calculus that represents accumulation or area under curves.