Answer:
65 cm
Explanation:
You want the perimeter of the shape that results from removing a 60° sector from a circle.
Curved edge
The curved edge of the shape is 5/6 of the circumference of the circle.
5/6C = 5/6(2πr) = 5/6·2·π·(9 cm) = 15π cm ≈ 47 cm
Straight edges
Each straight edge of the shape has a length equal to the radius. Then the straight edges have a total length of ...
2r = 2(9 cm) = 18 cm
Perimeter
The perimeter of the shape is the sum of the length of its curved edge and the lengths of the straight edges:
P = 47 cm + 18 cm = 65 cm
The perimeter is about 65 cm.
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Additional comment
A total circle is 360°, so 1/6 of the circle is 60°. The size of a sector of a circle can be described by the angle measure of its central angle. Here, that means the removed portion is a 60° sector.