# math

posted by .

the arc length and central angle of a circle are 10cm and 80degrees respectivly. what is the length of the radius?

• math -

Circumference of a circle

C = 2 r pi

the arc length

L = 2 r pi * theta / 360 °

= r * pi * theta / 180°

10 = r pi * 80 / 180 Multiply both sides by 180

10 * 180 = r * pi * 80

1800 = r * pi * 80 Divide both sides by 80 pi

1800 / 80 pi = r

r = 1800 / 80 pi

r = 40 * 45 / ( 40 * 2 * pi )

r = 45 / 2 pi

r = 45 / ( 2 * 3.14159 )

r = 45 / 6.28318

r = 7.162 cm

## Similar Questions

1. ### math

Whats the difference between an arc [of a circle]'s length and measure?
2. ### precalculus

The question is...find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Then it gives the radius r of 27 inches and an arc length s of 6 inches. How do I do that?
3. ### Trig

Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.?
4. ### math advanced functions

a) Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees, correct to one decimal place. b) Determine the arc length of …
5. ### algebra

of radius 54 meters subtended by the central angle 1/9 radian. s(arc length = meters How is the answer 6?
6. ### Math rem

2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o 3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm. 4. A circle …
7. ### Math Arc Length

Find the arc length corresponding to an angle of a degrees on a circle radius of 4.9 Enter the exact answer. I put the arc length was 4.9api/180 got it wrong. Any help?
8. ### math

In a circle with a radius of 5cm and is centered at point O, angle AOB intercepts arc AB. Arc AB has a length of 10cm. What is the degree measure of angle AOB?
9. ### apex geometry

Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true?
10. ### Geometry

A circle has a radius of 3 an arc in this circle has a central angle of 20 degrees what is the length of the arc

More Similar Questions