2004 AMC 12A Problem 9

Problem 9 of 25EasierAlgebra Geometry

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

25\%

without altering the volume, by what percent must the height be decreased?

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Solution

Multiplying the diameter by

\tfrac54

multiplies the base area by

\left(\tfrac54\right)^2 = \tfrac{25}{16}.

To keep the volume fixed, the height must be multiplied by

\tfrac{16}{25} = 0.64.

That is a decrease of

1 - 0.64 = 0.36,

36\%.

Thus, the correct answer is C.

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