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.

Components of a Truncated Cone

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.

Components of a Truncated Cone

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

Slant Height of a Truncated Cone Formula

Slant Height of a Truncated Cone Formula

Unfold of a Truncated Cone

Unfold of a Truncated Cone


Lateral Area of a Truncated Cone

Lateral Area of a Truncated Cone Formula

Surface Area of a Truncated Cone

Surface Area of a Truncated Cone Formula

Volume of a Truncated Cone

Volume of a Truncated Cone Formula

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.

Truncated Cone

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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.

Truncated Cone

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