The formula for finding the Slant height of a Cone is

The formula for finding the slant height l of a cone depends on the radius of the base (r) and the height of the cone (h). The slant height can be calculated using the Pythagorean theorem applied to the right triangle formed by the radius, height, and slant height.

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The slant height (l) of a cone is given by:

l = √(r^2 + h^2)

Where:

l is the slant height,
r is the radius of the base, and
h is the height of the cone.

What is Slant Height?

The slant height of a geometric figure, such as a cone or pyramid, is the distance measured along the lateral surface from the base to the apex (top) of the figure, along the "slant" or diagonal line. It's essentially the length of the side if you were to unroll the lateral surface into a flat shape.

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In the case of a cone, for example, the slant height is the distance from the base to the apex along the curved surface. In a pyramid, it's the distance from the base to the apex along one of the triangular faces.

The slant height is crucial for calculating various properties of these shapes, including surface area and volume.