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Geometry and Trigonometry Difficulty: Medium

Circle $K$ has a radius of $4 millimeters left parenthesis mm right parenthesis$ . Circle $L$ has an area of $100 pi mm squared$ . What is the total area, $in {mm}^{2}$ , of circles $K$ and $L$ ?

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Explanation

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

Choice A is incorrect. This is the sum of the radii, $in mm$ , of circles $K$ and $L$ multiplied by $π$ , not the total area, $in mm Superscript 2$ , of the circles.

Choice B is incorrect. This is the sum of the diameters, $in mm$ , of circles $K$ and $L$ multiplied by $π$ , not the total area, $in mm Superscript 2$ , of the circles.

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