Problem:
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by without altering the volume, by what percent must the height be decreased?
Answer Choices:
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B.
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E.
Solution:
Let , and , respectively, be the radius, height, and volume of the jar that is currently being used. The new jar will have a radius of and volume . Let be the height of the new jar. Then
Thus is of , so the height must be reduced by .
Multiplying the diameter by multiplies the area of the base by , so in order to keep the same volume, the height must be multiplied by . Thus the height must be decreased by , or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions