circle O int he above figure has a diameter of 6. if the central angle formed measures 60 deg , what is the lenght of the intercepted arc
2006-08-19 08:51:17 · 7 answers · asked by haxincrypt0naut 2 in Science & Mathematics ➔ Mathematics
The arc length of any circular segment can be found by multiplying the angle(in radian measure) by the radius. In equation form:
arc length = (radius) x (angle in radians)
In this case the diameter is 6 so the radius is 3. The angle is 60 deg, but we need to convert that to radians. We can convert from degrees to radians by multiplying by (pi/180deg). Doing this gives us:
60deg x (pi/180deg) = pi/3
Therefore the arc length is calculated by:
arc length = 3 x pi/3 = pi
The length of the intercepted arc is pi!
2006-08-19 09:10:00 · answer #1 · answered by josh 3 · 1⤊ 0⤋
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2016-12-11 09:07:57 · answer #2 · answered by ? 4 · 0⤊ 0⤋
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2016-10-05 10:54:04 · answer #3 · answered by gazdecki 4 · 0⤊ 0⤋
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circle O int he above figure has a diameter of 6. if the central angle formed measures 60 deg , what is the lenght of the intercepted arc
2015-08-10 12:34:47 · answer #4 · answered by Skyler 1 · 0⤊ 0⤋
The total length of the circle is pi multiplied by the diameter. If you use 3.14 as the value of pi, you get 18.84 units as the length of this circle. If you use a pi button on a calculator, you get a more exact answer. Now to find the length of the arc, multiply this number by the central angle divided by 360. (The bottom number is always 360, the total number of degrees in a circle.) 18.84 * (60/360) gives you 3.14. The reason we ended up back at pi is 60 degrees is 1/6 of a complete circle, and the diameter was 6. 6 multiplied by 1/6 is one.
2006-08-19 10:12:11 · answer #5 · answered by Animate M 1 · 0⤊ 1⤋
circumference = pi x diameter diameter = 20 circumference = 20pi 90/360 = 1/4 (360 degrees in a circle with a 90 degree arc) 20pi x 1/4 ( 1/4 of the circumference) 15.7 or 5pi
2016-03-13 05:43:08 · answer #6 · answered by ? 4 · 0⤊ 0⤋
All you need to is multiply the radius of the circle with the angle in radians. 60 degs is a 6th of the whole circumference, so the angle in radians is (1/6) * 2 * Pi. This makes the answer: 3 * (1/6) * 2 * Pi = Pi! (Since 3 * (1/6) * 2 = 1)
2006-08-19 09:02:46 · answer #7 · answered by nitro2k01 3 · 1⤊ 0⤋
Circumference is pi d = 6 pi. 60 degrees is 1/6 of a circle. So arc length is (6 pi)/6 = pi = 3.14.
2006-08-19 09:00:09 · answer #8 · answered by bpiguy 7 · 0⤊ 1⤋