Question

A cylinder has radius r and height h. a. How many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 2? 3? 5? 10? b. Describe the pattern in part (a). How many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 20?

Answer 1

To find it directly

A = 2 pi r h

A is proportional to rh

factor 2

A is multiplied by 2 * 2 = 4

factor 3

3 * 3 =9

factor 5

5 * 5 = 25

factor 10 

10 * 10 = 100

(b) the increase in A by factor x is x^2

c(20)^2 = 400