Mark H. answered • 10/03/19

Tutoring in Math and Science at all levels

It may be easiest to visualize this separately for each portion. A "tube" shape has an outer surface, inner surface, and 2 ends (which normally will be the same)

Working in __cm__

For the specified shape:

__Outer__: Simply the area of the outsdie of the larger cylinder, not counting the ends.

This is the circumference (c) times the length (l), C = pi*d, so the area is pi*60*300 = **pi*18000**

__Inner__: Simply the inner surface of the smaller cylinder: l is the same, and d is 20, so area = pi*20*300 = **p*6000**

__Ends__: Here we use the difference between the larger and smaller end areas.

for the larger: A = pi*d^{2} / 4 = pi*(60)^{2} / 4 = 900*pi

and the smaller: A = pi*(20)^{2} / 4 = 100*pi

difference: 800*pi

The are 2 ends so the total end area is **1600*pi**

**Add it all up: **A(total) = pi ( 18,000 + 6,000 + 1,600) = pi* 25,600 = **80424.7719319**

to one decimal place: **80424.8**