On the off chance that the question refers to a right cone,
l2 = r2 + h2 by Pythagoras, where l is the slant height, h the altitude and r the radius.
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A right circular cone with 8 height and 6 radius has a slant height of 10.
There is no single equation. There are different equations for its volume, surface area, vertical height, slant height, base radius, and so on and some of these depend on what information is available.
Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.
Slant height is 7.81 inches.