How can I find the surface area of a right cone with a radius of 6 and slant height of 16

First, you have to calculate the height.

Pythagorean Theorem:

a^2+b^2=c^2

Slant height=c^2

Radius=b^2

So, a^2+6^2=16^2

a^2+36=256

a^2=220

a=14.832397

Surface Area = πr (r + square root of h^2+r^2)

Surface Area is approximately 414.69