Slant Height of Frustum of Cone Calculator

Formula

The formula to calculate the Slant Height of Frustum of Cone (hSlant) is:

\[ hSlant = \sqrt{h^2 + (rTop - rBase)^2} \]

Where:

\(hSlant\) is the Slant Height of Frustum of Cone (measured in meters).
\(h\) is the Height of Frustum of Cone (measured in meters).
\(rTop\) is the Top Radius of Frustum of Cone (measured in meters).
\(rBase\) is the Base Radius of Frustum of Cone (measured in meters).

Definition

The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.

Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.

How to calculate Slant Height of Frustum of Cone

Let's assume the following values:

Height of Frustum of Cone (h) = 8 meters
Top Radius of Frustum of Cone (rTop) = 10 meters
Base Radius of Frustum of Cone (rBase) = 5 meters

Using the formula:

\[ hSlant = \sqrt{8^2 + (10 - 5)^2} \]

Evaluating:

\[ hSlant \approx 9.434 \, \text{meters} \]

The Slant Height of Frustum of Cone is approximately 9.434 meters.

Conversion Chart

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Height (h) (meters)	Top Radius (rTop) (meters)	Base Radius (rBase) (meters)	Slant Height (hSlant) (meters)