A circle has a radius of 9 cm. A central angle measures 315 degrees. ?

Question

Determine the arc lenth subtended by two radii making the central angle. Round your answer to the nearest tenth of a centimeter.

Answer 1

A circle has a radius of 9 cm.

A central angle measures 315 degrees.

Determine the arc length subtended by two radii making the central angle.

2 pi * 9 (315/360) cm = 49.4800843 cm or

49.5 cm (rounded to the nearest tenth of a centimeter).  

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Answer 2

315 / 360 * pi * radius

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Answer 3

What's the circumference of a full circle with a 9 cm radius?

C = 2πr

C = 2π*9

C = 18π cm

But you don't want a full 360°, you just want 315°. So multiply by 315/360. We can reduce that fraction if you like by dividing top and bottom by 45.

315/360

= 7/8

So take 7/8 of the full circumference:

arc = 7/8 * 18π cm

arc = 7/4 * 9π cm

arc = 63π / 4

arc ≈  49.48 cm

Answer (to the nearest tenth of a centimeter)

~49.5 cm

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Answer 4

s = rθ, where θ is measured in radians.

θ = (315 / 180)π radians = 7π/4 radians

s = 9(7π/4) = 63π/4 = 49.5 cm

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Answer 5

2 * pi * 9 * (315/360) =>

18 * pi * (7/8) =>

9 * pi * 7 / 4 =>

63 * pi / 4 =>

49.4800...

49.5

Or

(63/4) * pi =>

(63/4) * (22/7), roughly

(63/7) * (22/4) =>

9 * 11/2 =>

99/2 =>

49.5

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