SOLUTION: Why can you find an excact Surface Area measurement for a prism but not a cylinder

Question 275765: Why can you find an excact Surface Area measurement for a prism but not a cylinder
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The underlying premise of your question is not true in general.

In the first place, you can never find the exact measurement of anything. ALL measurements are approximate, no matter how precisely taken. Therefore you can never exactly represent the surface area of a prism because the measurements of the edges begin as approximations.

On the other hand, who says you cannot represent the surface area of a cylinder exactly? Typically the surface area calculation for a cylinder involves

, the ratio of the circumference of a circle to its diameter.

is a transcendental irrational number, and irrational numbers can never be represented by an exact decimal fraction. However, that is not to say that you cannot represent a quantity involving

exactly, because you can. All you need to do is leave the result in terms of

and you have your exact representation. So presuming an ideal theoretical cylinder whose height was exactly

and base radius exactly

, you would have a lateral surface area of exactly

or a total surface area of exactly

. Example: If you had a cylinder that was purported to be exactly 5 units in height and exactly 2 units in radius (even though no one would ever be able to measure it and determine whether it was indeed 5 high and 2 in radius), then the lateral surface area would be exactly

, and the total surface area would be exactly

John

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