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Note: If you are working with angles measured in degrees, instead of in radians, then you'll need to include an extra conversion factor:
Confession: A big part of the reason that I've explained the relationship between the circle formulas and the sector formulas is that I could never keep track of the sectorarea and arclength formulas; I was always forgetting them or messing them up. But I could always remember the formulas for the area and circumference of an entire circle. So I learned (the hard way) that, by keeping the above relationship in mind, noting where the angles go in the wholecircle formulas, it is possible always to keep things straight.
1. Given a circle with radius r = 8 units and a sector with subtended angle measuring 45°, find the area of the sector and the length of the arc.
They've given me the radius and the central angle, so I can just plug straight into the formulas, and simplify to get my answers. For convenience, I'll first convert "45°" to the corresponding radian value of π/4. Then I'll do my plugnchug:
Then answer is:
area A = 8π square units, arclength s = 2π units
2. Given a sector with radius r = 3 cm and a corresponding arc length of 5π radians, find the area of the sector.
3. A circle's sector has an area of 108 cm2, and the sector intercepts an arc with length 12 cm. Find the diameter of the circle.
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