Frustum

Definition

A frustum is a portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it. It is characterized by having two bases, which are parallel to each other, and a lateral surface connecting them.

5 Must Know Facts For Your Next Test

1. The volume of a frustum can be calculated using the formula $V = \frac{1}{3}h(A_1 + A_2 + \sqrt{A_1A_2})$, where $h$ is the height, and $A_1$ and $A_2$ are the areas of the two bases.
2. The lateral surface area of a frustum of a cone is given by $\pi(R + r)s$, where $R$ and $r$ are the radii of the two bases, and $s$ is the slant height.
3. In calculus, a frustum can be used to approximate volumes of solids by integrating cross-sectional areas.
4. The concept of a frustum is essential when studying solids of revolution in integral calculus.
5. To derive formulas involving frustums, you often need to use principles from geometry, such as similar triangles.

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?
• Why are frustums important when dealing with solids of revolution?

Related terms

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

Slant Height: The distance measured along the lateral surface from one base to another in a conical or pyramidal shape.

Cross-Sectional Area: \text{The area obtained by slicing through an object perpendicular to an axis.}