Find the surface area of the cylinder in terms of Pi 6in and 12in

the correct question is 
Find the surface area of a cylinder in terms of pi with a radius of 6 in and a height of 12 in

we now that
[surface area of a cylinder]=2*[area of the base]+perimeter of the base*height 

area of the base=pi*r²
r=6 in
area of the base=pi*6²------> 36*pi in²

perimeter of the base=2*pi*r-------> 2*pi*6-----> 12*pi in
height=12 in

[surface area of a cylinder]=2*[36*pi]+12*pi*12-----> 72*pi+144*pi
[surface area of a cylinder]=216*pi in² 

the answer is
The surface area of a cylinder is 216*pi in²