Answer:
total area = 1056 π inch²
Explanation:
Suppose you could cut away the top and bottom of the drum with a big tin opener
Their surfaces is easy to calculate:
2 * ( π * 12² ) = 288π inch²
Now you need to find the area of the big toilet role like drum.
Suppose you could cut the whole 32 inch height of the drum, with a huge scissors. Because it is cut, you can flatten it out, and lay it out on the surface.
You now have a rectangle of height 32 inch. Because it used to be round on the top and bottom, the width is known as the circumference of that circle with radius 12 inch or 2*π*12 = 24 π
area rectangle
height 32 inch
width 24 π inch
area = 32 * 24 π inch²
area = 768 π inch²
now add the area of the top and bottom :
total area (288 π + 768 π )inch²
total area = 1056 π inch²