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?

Step 1 (Volume Formula): The volume of a cylinder is given by $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step 2 (Changes in Dimensions): The diameter (and therefore the radius) is increased by $25\%$. Let the new radius be $r^{\prime }$:

Since the volume remains constant ($V^{\prime }=V$):

Step 3 (Decrease in height): The height is reduced from $h$ to $0.64h$, which is a decrease of:

Therefore, the height must be decreased by $36\%$.