To find the rate at which the area of the circle is changing ($\frac{dA}{dt}$) when the radius is 22 mm:

Formula:

The area of a circle is $A = \pi r^2$.
Differentiate with respect to $t$: $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$

Known values:

• $r = 22 \, \text{mm}$
• $\frac{dr}{dt} = 5 \, \text{mm/s}$

Calculation:

$\frac{dA}{dt} = 2\pi (22)(5)$ $\frac{dA}{dt} = 220\pi \, \text{mm}^2/\text{s}$ Using $\pi \approx 3.14159$: $\frac{dA}{dt} \approx 220 \cdot 3.14159 = 691.15 \, \text{mm}^2/\text{s}$

Final Answer:

$\boxed{691.150 \, \text{mm}^2/\text{s}}$