Circle K has a radius of 4   millimeters   mm . Circle L has an area of 100 π

Question

Circle K has a radius of 4 &#160; millimeters &#160; mm . Circle L has an area of 100 &#960; &#160; mm 2 . What is the total area, in &#160; mm 2 , of circles K and L ?

Accepted Answer

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&rsquo;s given that circle K has a radius of 4 millimeters mm . Substituting 4 for r in the formula A = &pi; r 2 yields A = &pi; 4 2 , or A = 16 &pi; . Therefore, the area of circle K is 16 &pi; mm 2 . It&rsquo;s given that circle L has an area of 100 &pi; mm 2 . Therefore, the total area, 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, in mm , of circles K and L multiplied by &pi; , not the total area, in mm 2 , of the circles. Choice B is incorrect. This is the sum of the diameters, in mm , of circles K and L multiplied by &pi; , not the total area, in mm 2 , of the circles. Choice C is incorrect and may result from conceptual or calculation errors.

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