Answer:
walk area = 125.6 m²
Explanation:
You are asked for the area of a sidewalk of given width that is around a circle of given radius. The pattern you're asked to fill in would have you compute the area of the inner circle, and of the outer circle, then find the difference between the areas.
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The formula for the area of a circle is ...
A = πr²
bigger circle
The radius is shown as 11 m, so its area is ...
A = π(11 m)² = 121π m² = 379.94 m²
smaller circle
The radius is shown as 9 m, so its area is ...
A = π(9 m)² = 81π m² = 254.34 m²
area difference
The difference between the two areas is ...
walk area = big circle area - small circle area
walk area = 379.94 m² -254.34 m² = 125.6 m²
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Additional comment
The area can also be computed by multiplying the centerline length of the sidewalk by its width. The center of the walk is (9+11)/2 = 10 m from the centers of the circles, so the circumference (centerline length) is
C = 2πr = 2(3.14)(10 m) = 62.8 m
The width of the sidewalk is 11 -9 = 2 meters, so its area is ...
(2 m)(62.8 m) = 125.6 m² . . . . sidewalk area