The surface area of a cylinder is increasing by 2 pi square inches per hour and the height is decreasing by 0.1 inches per hour when the radius is 16 inches and the height is 7 inches. how fast is the radius of the cylinder changing?

The decreasing part area : 0.1*2*Pi*r

＝0.2 Pi r

The increasing part is 2 pi square.

the top and bottom area now: 2pi * (16＋X)

X means the increasing inches.

Then use the top and bottom part miners the decreasing equals to the the increasing part. Then the answer you can calculate by yourself ...