A circle sector has a 21 cm radius and a 135° central angle. Find its perimeter.
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Answer: A. 91.5 cm
Explanation
Calculating the arc length of the sector using one thirty fifth over three hundred sixty gives forty nine point five. Adding the two bounding radii lengths of forty two centimeters to the arc length gives ninety one point five. The total perimeter of a circular sector combines the curved arc length with two straight radius segments. The perimeter of a sector includes both its curved outer arc and the two straight edge radii. Arc length is determined by multiplying the circumference by the central angle fraction. The radius measurement is multiplied by two because two straight edges enclose the sector.
Pizza parlor cutting practices require calculating sector perimeters and arc lengths for packaging design. Mechanical engineers design rotating machine cams with specific sector angles and perimeter boundaries. Landscaping irrigation systems spray water in circular sectors requiring perimeter boundary calculations. Option b overestimates the perimeter due to a minor arithmetic error in the arc length fraction. Option c calculates a higher value by incorrectly rounding up the arc length component. Option d results from miscalculating the radius addition portion of the sector perimeter.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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