The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is

Given,

Let Initial height of cylinder = h

Initial curved surface area = 2πrh

Now altitude become = 6h

And base area =

In first case radius = r

In second case it become =

So , area =

Factor by which lateral surface of cylinder increase =