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Slant Height Formula
Before learning the slant height formula, let us see what is slant height. The slant height of an object (such as a cone, or pyramid) is the distance along the curved surface, drawn from the edge at the top to a point on the circumference of the circle at the base. In other words, The slant height is the shortest possible distance from the base to the apex along the surface of the solid, denoted either as s or l. The slant height formula helps in the calculation of the slant height in any object.
What is the Slant Height Formula?
The slant height formulas are usually defined for cone and pyramid. They are as follows:
Slant Height of Cone
The slant height formula of a cone is given as:
s^{2} = h^{2} + r^{2}
or,
\( s = \sqrt{h^2 + r^2}\)
Slant Height Formula of Pyramid
(Slant height)^{2} = (Height)^{2} + Base/2)^{2}
or,
\( s = \sqrt{h^2 + \frac{b}{2}^2}\)
In the above two formulas,
 s = slant height
 h = vertical height
 b = base
Let us see how to apply the slant height formula in the following solved examples.
Solved Examples Using Slant Height Formula

Example 1: The height and base of a square pyramid measure 8m and 12m respectively. Calculate its slant height.
Solution:
To find: Slant height of square pyramid
Given: Height of pyramid = 8m
Base of pyramid = 12m
Using slant height formula,
s^{2} = (8)^{2} + (12/2)^{2}
s^{2} = 100
s = 10m
Answer: Slant height, s = 10 m

Example 2: The height and base radius of a circular cone measure 4 m and 3 m respectively. Calculate its slant height.
Solution:
To find: Slant height of cone
Given:
Height of cone = 4 m
Base radius of cone = 3 m
Using slant height formula,
s^{2} = (4)^{2} + (3)^{2}
s^{2} = 25
s = 5 m
Answer: Slant height, s = 5 m
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