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Answer:
1. area DEF = 2π cm²
2. arc JK = 2π cm
Step-by-step explanation:
1. The area is given by ...
A = 1/2r²θ . . . . . where r is the radius and θ is the central angle in radians
Your sector has an area of ...
A = (1/2)(3 cm)²(80(π/180)) = (1/2)(9 cm²)(4/9π)
A = 2π cm²
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2. The length of an arc is ...
s = rθ . . . . . . . where r is the radius and θ is the central angle in radians
s = (5 cm)(72(π/180)) = (5 cm)(2/5π)
s = 2π cm . . . arc length
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<em>Additional comment</em>
There are π radians in 180°, so an angle in degrees can be converted to an angle in radians by multiplying by π/180°. (The units of degrees cancel, leaving a pure number. "Radians" have no units.)
