If a cylinder's radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?

We let

r1 = the original radius of the cylinder

r2 = the new radius of the cylinder

h1 = the original height of the cylinder

h2 = the new height of the cylinder

SA = surface are of the cylinder

the radius and the height are shrunk down to a third of their value therefore

r2 = r1/3

h2 = h1/3

SA = 2 (PI) r^2 + 2 (PI) rh

SA = 2 (PI) [ (r1^2) / 9] + 2 (PI) (r1/3) (h1/3)

Simplifying

SA = [2 (PI) r]/9 * (r1 + h1)