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Find the arc length and area of a sector with radius r=13 inches and central angle theta =40 degrees

User Meloncholy
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4 votes

Answer:

The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.

Explanation:

Geometrically speaking, we determine the arc length (
s), in inches, and the area (
A), in square inches, of a circle sector by means of these formulas:


s = 2\pi\cdot \left((\theta)/(360)\right)\cdot r (1)


A = \pi \cdot \left((\theta)/(360) \right)\cdot r^(2) (2)

Where:


r - Radius, in inches.


\theta - Central angle, in sexagesimal degrees.

If we know that
\theta = 40^(\circ) and
r = 13\,in, then the arc length and the area of the circle sector are, respectively:


s = 2\pi\cdot \left((40)/(360) \right)\cdot (13\,in)


s \approx 9.076\,in


A = \pi \cdot \left((40)/(360) \right)\cdot (13\,in)^(2)


A = 58.992\,in^(2)

The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.

User RubbleFord
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