This video shows how to find the surface area of a cone when the slant height IS given and when it is NOT given. The Pythagorean Theorem is used to find the missing slant height to calculate the total surface area of a cone.
Yes just take length( which is the square root of height squared plus radius squared ) and make that the upper bound , then along that length you can get each height if you calculate the angle. So the integral will be xsin(angle) from 0-L , then multiplied by 2pi and added to area of base.
