Circle K has a radius of 4   millimeters   mm . Circle L has an

Choice D is correct. The area, $A$, of a circle is given by the formula $A=\pi r^2$, where $r$ represents the radius of the circle. It’s given that circle $K$ has a radius of $4 \text{millimeters} \left(\text{mm}\right)$. Substituting $4$ for $r$ in the formula $A=\pi r^2$ yields $A=\pi {\left(4\right)}^2$, or $A=16\pi$. Therefore, the area of circle $K$ is $16\pi {\text{mm}}^2$. It’s given that circle $L$ has an area of $100\pi {\text{mm}}^2$. Therefore, the total area, ${\text{in mm}}^2$, of circles $K$ and $L$ is $16\pi +100\pi$, or $116\pi$.

Choice A is incorrect. This is the sum of the radii, $\text{in mm}$, of circles $K$ and $L$ multiplied by $\pi$, not the total area, ${\text{in mm}}^2$, of the circles.

Choice B is incorrect. This is the sum of the diameters, $\text{in mm}$, of circles $K$ and $L$ multiplied by $\pi$, not the total area, ${\text{in mm}}^2$, of the circles.

Choice C is incorrect and may result from conceptual or calculation errors.