Question

Cylinder A has radius 4 times the radius of cylinder B, and height 4 times the height of cylinder B.

What is the ratio of the lateral area of A to the lateral area of B?

Answer 1

The surface areas of two similar shapes are proportional to
the squares of their corresponding sides

S(Cylinder 1)/S(cylinder 2) = 4^2/1^2 = 16
So A's surface area is 16 times that of B's surface

or, the long way ...

cylinder B: radius -- r, height --- h
cylinder A: radius = 4r, height = 4h

surface area of A = 2πr^2 + 2πrh = <b>2</b>(πr^2 + πrh)
surface area of B = 2π(16r^2) + 2π(4r)(4h)
= 32πr^2 + 32πrh = <b>32</b>(πr^2 + πrh) or 16 times that of A