To find the width,imaginetakinga can-likecylinderapartwith a scissors.Whenyou cut the lateralarea,
you see that it is equalto the circumferenceof the can’s top. The circumferenceof a circleis givenby
the lateralarea,L, is
Now we can find the area of the entirecylinderusing
.
You can see that the formulawe usedto find the total surfacearea can be usedfor any right cylinder.
Areaof a RightCylinderThe surfacearea of a right cylinder, with radius and height
is givenby , where is the area of eachbaseof the cylinderand
is the lateralarea of the cylinder.Example 1
Use a net to find the surfacearea of the cylinder.First drawand labela net for the figure.Calculatethe area of eachbase.