SOLUTION: having trouble with this problem: Michael had $10 to spend on popcorn at the movies. He had to choose between buying two small cylindrical containers at $5 each or one large cyli

Question 1048655: having trouble with this problem: Michael had $10 to spend on popcorn at the movies. He had to choose between buying two small cylindrical containers at $5 each or one large cylindrical container for $10. He noticed that the large container was 2/3 the height of the small container, but that the diameter of the large container looked about twice as long as the diameter of the small container. He bought the large container then asked his math class if he'd made the right choice. Did he make the right choice? Explain why or why not.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the radius of the smaller container. Then the radius of the larger container is

. Let

represent the height of the smaller container and then the height of the larger container is

The volume of the larger container is then

.

The volume of the smaller container is

, and the volume of 2 of the smaller containers must be

Divide the volume of the larger by the volume of the two smaller containers. If you get a value larger than 1, it is a good deal. If you get a value less than 1, you made a bad choice. Equal to 1 is a wash.

Notice that all of the variables and

cancel.

John

My calculator said it, I believe it, that settles it

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