# Frustum of a Cone

A **frustum of a cone** or **truncated cone** is the result of cutting a **cone** by a plane parallel to the base and removing the part containing the apex.

The **height** is the line segment that joins the two bases perpendicularly.

The **radii** are the radii of their bases.

The **slant height** is the shortest possible distance between the edges of the two bases.

The **slant height** of the truncated cone is obtained by applying the Pythagorean theorem for the shaded triangle:

#### Unfold of a Truncated Cone

### Lateral Area of a Truncated Cone

### Surface Area of a Truncated Cone

### Volume of a Truncated Cone

#### Examples

Calculate the lateral area, surface area and volume of a truncated cone of radii 2 and 6 cm and a of height 10 cm.

Calculate the lateral area, surface area and volume of a truncated cone of radii 10 and 12 cm and a slant height of 15 cm.

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