I'm going to improve your answer:
Since I don't know how, I would ask my math teacher how. I have a prolem for homework where it wants me to find it with out the Lateral Area or the entire surface are.. :( Good luck :)
To find the slant height of an object (frustum or pyramid) you take the distance measured along a lateral face from the base to the apex along the centre of the face or in other words it is the altitude (height) of the triangle comprising a lateral face. (Kern and Bland 1948,p 50)
Why do you need to FIND the slant height if you have the [lateral height and] slant height?
the slant height is always 2 units bigger then the height
(slant height)2= (height)2+(1/2 side)2
Knowing the slant height helps because it represents the height of the triangle that makes up each lateral face. So, the slant height helps you to find the surface area of each lateral face.
Slant height is 39.98 cm
Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.
The height would be The square root of the square of the slant surface length minus the square of the radius of the cone at the base.
I don't know not mine
the slant height is always 2 units bigger then the height
By using trigonometry or Pythagoras' theorem
Uisng the lateral area and tha radius, you should be able to find the height of the cone. Using the height and radius as the legs of a right triangle, use the Pythagorean Theorem. The hypotenuse is the slant height.