First we find slant height l of cone to find total surface area and leteral surface area. To find slant hieght we find relation between radius r, perpedicular hieght h, slant hieght l.
l,r,h makes a right angle triangle in cone whose hypotenious is l so relation will be,
l² =r² +h²
l = ( 16² + 12²)^1/2
l =( 256 + 144 )^1/2
l = 20 unit.

We take a circular disk. It's center O then we draw two points on circumfrance of circular disk A and B. Then we join these point to center O then the line will be OA and OB and AOB sector is formed. OA and OB is the radius of this circular disk OA = l unit then we cut sector AOB and throw it then left over shape is not a circular disk.

There is a gap between OA and OB. Bring OA and OB lines of the left over disk together. So that line OA and OB superimpose over each other.
In this situation points A and B will meet and the circular part of the left over disk will form a circle and point O will be away from this circle.
This will looks like a cone. The circular lenght of the left over disk becomes the circumfrance of the base of the cone is equal to 2(22/7)r and the slant height of the cone is equal to OA = OB =radius of the left over circular disk.

So lateral surface area of cone =Area of the left over disk =1/2 x circular length of the disk x radius of the disk.
1/2 x 2(22/7)r x l = (22/7)r.l
=1005.7142857143 unit.

Total surface area of cone =letral suface area +Area of base surface of cone.
(22/7)r.l + (22/7)r²
(22/7)r[l + r] =50.285714285714 x 36 = 1810.2857142857 unit.