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Question 935322: I'm having trouble answering this question? Can anyone help Please..
Suppose you double the radius of a right cylinder. How does that affect the lateral area? How does it affect the surface area? Explain why the surface area is not doubled using the proper formula.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The lateral area is just the area of the curved sides of the cylinder.
It does not include the bases.
It is like the area of the label on a can of soup.
It is calculated by multiplying the circumference of the base times the height of the right cylinder:
  .
The formula in your book may be something like
 .
As the radius is doubled, the circumference of the base doubles,
but the height has not been changed,
so the lateral area is just doubled.
If cylinder number 1 has  , then  is its lateral area.
If you double the radius to make cylinder number 2, with  ,
that cylinder has a lateral area of
 -->  -->  .
Each base (top and bottom) is a circle of area
The total surface area of the cylinder is the lateral area plus the area of the bases:
 or  .
As the radius is doubled, the area of each base quadruples,
making the total area more than double.
If cylinder number 1 has , then  is its total surface area.
If you double the radius to make cylinder number 2, with ,
that cylinder has a surface area of
 -->  -->  -->  -->  -->  .
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