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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 sector-area and arc-length 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 whole-circle 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 plug-n-chug:
Then answer is:
area A = 8π square units, arc-length 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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