Suppose one right circular cylinder has radius 2 m and height 6 m and another had radius 6 m and height 2 m

Question

a. Which cylinder has the greatest lateral surface area?

b. Which cylinder has the greater total surface area?

Answer 1

Lateral area = circumference * height

= pi*2*radius * height

THeir respective lateral areas are pi*2*2*6 = 24*pi and pi*2*6*2 = 24*pi

(It's a tie)

Total surface area is 2*pi*radius^2 + pi*2*radius*height.

Their surface areas are respectively 2*pi*2^2 + pi*2*6 = 8*pi + 12*pi = 20*pi

and 2*pi*6^2 + pi*2*6*2 = 72*pi + 24*pi = 96*pi

(2nd cylinder has larger surface area)