



Now we
know how to find the volume



of
some objects. 





Next
we will see how to find 


the
area of the surface of those objects. 





First
the cube. 





A
cube is made up of six equal sized squares ... 











Find
the area of one of the squares 


multiply
by six 


and
BINGO! 


You're
done. 





Example: 


Find
the area of the surface of this cube ... 











The
sides are 5 units each. 


The
area of one surface is ... 





5
×
5 = 25






There
are six faces on the surface 


so
the area of the entire surface is ... 


25 ×
6 = 150






Example: 


Find
the area of the surface 


of
this rectangular solid object ... 











There
are two ways to calculate this one. 


The
top and bottom surfaces are 5 x 5 = 25 units each. 


The
four side faces are 8 x 5 = 40 units each. 





2
×
25 + 4 ×
40 = 210






The
other way to calculate this one 


starts
out the same way. 





The
top and bottom surfaces are 5 x 5 = 25 units each. 


Then
... 


The
perimeter of the bottom surface 


is
5 + 5 + 5 + 5 = 20 units. 


Multiply
this times the height (8) 


and
we get the area of the surface 


of
all 4 sides all at the same time. 


20
x 8 = 160. 


Add
that to the area of the top and bottom ... 





2 ×
25 + 160 =
210 





Example: 


Find
the area of the surface of the cylinder 











This
is why we used that goofy second method 


in
that last example. 


We
need it for stuff like this cylinder. 





The
areas of the top and the bottom 


of
the cylinder are each: 






Area = pr^{2} 



Area = 9p 



Area »
28.274 





To
find the area of the side, 


we
first need to find the circumference of the circle ... 





Circumference = p
×
diameter 





The
radius equals 3, 


so
the diameter equals 6 ... 






Circumference = p
×
6 



Circumference »
18.850 





The
area of the side is equal to 


the
circumference of the base 


times
the height. 






Area of the side »
18.850 ×
10 



Area of the side »
188.50 





The
total area of the surface of the cylinder 


is
equal to the area of the top and bottom 


plus
the area of the side. 





28.274 + 28.274
+ 188.50 = 245.048 





Sometimes
we just need to find the area on the side. 


Math
types wanted a fancy way "the area on the side." 


They
came up with the term LATERAL AREA. 


Lateral
means something like "on the side." 





OK,
then give me a ham on rye with LATERAL mayo! 





Ha
ha ha, how funny. Can we get back to math now? 





Just
remember that if somewhere (like on a test maybe) 


they
ask you for the LATERAL AREA, 


they
don't want the are on the top and the bottom. 


They
only want the mayo. 





copyright 2005 Bruce Kirkpatrick 
