Question

The lateral area of a cylinder is 100pi in^2. If its dimensions are reduced to one-fifth their original length, what would its new area be?

Answer 1

4pi in^2

Explanation:

Lateral surface area of a cylinder = 2πrh

π = pi

r = radius

h = height

Let me illustrate with an example

A cylinder has the following dimensions

r = radius = 20

h = height = 10

lateral area = 2 x π x 20 x 10 = 400π

If dimensions are reduced to one-fifth their original length, new dimensions are

r = radius = 20 x 1/5 = 4

h = height = 10 x 1/5 = 2

New lateral area = 2 x 4 x 2 x π = 16π

change in lateral area = 400π / 16π = 25

If dimensions are reduced by 1/5, lateral area would reduce by 25

100 pi / 25 = 4