You included the area of the circular base.
I understood that "lateral surface area" excluded the base of the solid.
For the volume I got pi(6^2)(8)/3 = 301.5929
mmmmh, now would that be a coincidence that this answer is the same as the one you got for the total surface area???
so its the same???
no, just a simple coincidence with those numbers.
I tried it with a cone of height 12 and radius 5, resulting in a slant height of 13
the total surface area would be 65pi + 25pi = 90pi and
the volume would be 25pi(12)/3 = 100pi
All we need in one exception to our perceived relationship and it is pooched.