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

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.

2004 AMC 10A Problem 11

Answer: C

Difficulty rating: 1310

Solution:

Problem 11 in Other Years