Mathematics

This is a related rates problem where you need to connect how the radius changes to how the area changes. Since area depends on radius through the formula $A = \pi r^2$, a shrinking radius will shrink the area—but the key is understanding why mathematically. Take the derivative of the area formula with respect to time to see the relationship between $\frac{dA}{dt}$ and $\frac{dr}{dt}$, then substitute the given values to determine the sign of the rate of change.

This is a related rates problem where you need to connect how the radius changes to how the area changes. Since area depends on radius through the formula $A = \pi r^2$, a shrinking radius will shrink the area—but the key is understanding why mathematically. Take the derivative of the area formula with respect to time to see the relationship between $\frac{dA}{dt}$ and $\frac{dr}{dt}$, then substitute the given values to determine the sign of the rate of change.