Question

The altitude of a circular cylinder is increased 12 times and the base area is decreased to one ninth of its value. The factor by which the lateral surface area of the cylinder increases is:

Answer 1

Curved surface area of cylinder = 2 πrh

Height is increased to 6 times = 6h

Base area is decreased to (1/9th) i.e. straight r space equals space 1 third straight r

Now,

New curved surface area = 2 straight pi space cross times space 1 third straight r space cross times space 6 straight h

i.e left parenthesis 2 πrh right parenthesis space cross times space 2

∴ Lateral surface area becomes twice.