How to find the slant height of a cone if the height of the cone is 8cm

I want to find the curved surface area of a cone.
The height of the cone = 8cm
The radius of the cone = 6cm

Imagine a cone. imagine a right angled triangle made by the axis (height of cone), radius of base, and slant height. The slant height will act as hypotenuse. so

(base radius)^2 + (height)^2 = (Slant Height)^2

(6cm)^2 + (8cm)^2 = (Slant Height)^2

36cm square + 64 cm square = (Slant Height)^2

(Slant Height)^2 = 100 cm square

Slant Height = √100 cm square = 10 cm

So, the Slant height comes out to be 10 cm

pythagorean theorum:
a^2 + b^2 = c^2
(8)^2 + (6)^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c

To find the curved surface area:
This formula has been long forgotten with the depths of time and space.
Translation: The last time I've used it was math class last year

Basically u make a right triangle inside the cone using the slant height S as the hypotenuse 8cm and 6cm r ur legs. Use Pythagorean theorem 8 squared +6 squared = S squared. 64+36=S squared. 100=S squared S=10

By Pythagoras
(Slant height)^2 = h^2 + r^2 = 8^2 + 6^2
Slant height = sqrt(64 + 36) = 10 cm