2004 AMC 10A Problem 11

Question

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?

10

25

36

50

60

Answer: C

Concepts:cylinder volume percentage

Difficulty rating: 1310

Small hint:

The volume

\pi r^2 h

is unchanged, so

r^2 h

stays fixed

Big hint:

Multiplying the radius by

1.25

multiplies

r^2

by

1.25^2

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.