The correct answer or the difference between the area of the region with the largest area and the area of the region with the smallest area of the given concentric circles is 7[tex]\pi[/tex].
Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words. An annulus is the space between two concentric circles with dissimilar radii.
For region X:
Radius of the circle or r = 4units
Area of region X = [tex]\pi r^{2}[/tex] = [tex]\pi 4^{2}[/tex] = [tex]16\pi[/tex]
For region Y:
Radius of the circle or R = 6units
Area of region Y= [tex]\pi R^{2} - \pi r^{2} = \pi 6^{2} -\pi 4^{2} = 36\pi -16\pi[/tex] = [tex]20\pi[/tex]
For region Z:
Radius of the circle or R* = 7units
Area of region Z = [tex]\pi R^*^{2} -\pi R^{2} =\pi 7^{2} -\pi 6^{2} = 49\pi -36\pi =13\pi[/tex]
the difference between the area of the region with the largest area and the area of the region with the smallest area of the given concentric circles = [tex]20\pi -13\pi[/tex] = [tex]7\pi[/tex]
Hence, the difference between the area of the region with the largest area and the area of the region with the smallest area is [tex]7\pi[/tex].
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