2004 AMC 10A Problem 11

Problem 11 of 25IntermediateAlgebra 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

Keeping

\pi r^2 h

constant while multiplying the radius by

1.25

requires the height to be multiplied by

\dfrac{1}{1.25^2} = \dfrac{1}{1.5625} = 0.64.

So the height becomes

64\%

of the original, a decrease of

36\%.

Thus, the correct answer is C.

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