Answer:
527.52 cm²
Explanation:
You want the area of the region between circles of diameter 46 cm and 38 cm.
Area
The area of the ring is the difference between the area of the outer circle and the area of the inner circle.
The area of a circle of diameter d is given by ...
A = (π/4)d²
Then the difference in areas is ...
A = (π/4)(d2² -d1²) = (3.14/4)(46² -38²) = 527.52 . . . . cm²
The area of the shaded region is 527.52 cm².
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Additional comment
This can be described as a "composite" shape. It is a combination of a positive shape (the outer circle) and a negative shape (the inner circle). The area will be the signed sum of the areas of those shapes.
There are many applications of this sort of thinking. For example, the area of an L-shape can be considered to be the area of the outer rectangle, less the area of the rectangular corner cutout.
The area of a "donut" like this can also be figured as the product of the centerline length of the ring (42π cm) and the width of the ring (4 cm). Sometimes, this is easier to see, especially if radii are given instead of diameters.
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