Question

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23
Central angle BAC of circle A measures 20" radians. Arc BC has a length of 63.487 centimeters. What is the radius of the circle?
The radius of circle A is ✓ centimeters.

Answer 1

Answer: 55.2

Explanation:

got it correct on my test!

Answer 2

r = 55.2 cm

Explanation:

the arc length is calculated as

arc = circumference × fraction of circle

= 2πr ×
`((23)/(20)\pi )/(2\pi )` ( r is the radius )

given arc = 63.48π , then

2πr ×
`((23)/(20)\pi )/(2\pi )` = 63.48π ( cancel 2π on numerator/ denominator )

r ×
`(23)/(20)` π = 63.48π ( divide both sides by π )

`(23r)/(20)` = 63.48 ( multiply both sides by 20 to clear the fraction )

23r = 1269.6 ( divide both sides by 23 )

r = 55.2 cm