Question

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?

Answer 1

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)