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Q: If the radius of a circle is m what is the length of an arc of the circle intercepted by a central angle of pi radians?

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The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.

arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.

Length of arc: 115/360 times (130pi) = 130.5 inches rounded

You can think of an arc as a fraction of the circumferance of a circle. Also, a complete circle is 2pi radians, so any central angle is THETA / 2pi of a complete circle. Multiply by the circumferance to get the length of the arc: THETA / 2pi * 2(pi)(r) = THETA * r or the length of the arc is simply the radius times the central angle in radians

The angles measured in radians are about 57.3 degrees. A measurement of an angle in radians is equal to the length of its corresponding arc in the circle.

Related questions

The formula for calculating the circumference of a circle is 2πr, where r is the radius of the circle and π is 3.1415926535890793 - usually shorted to either 3.1416 or 3.14 So that the circumference of a circle with a radius of 10 units is 62.83 units There are pi radians in a half of a circle. Thus, the measure of a central angle which is a straight line is pi radians. We have a formula that show that the length of an intercepted arc is equal to the product of the angle in radians that intercepts that arc, with the length of the radius of the circle. So we can say that the length of a semicircle is (pi)(r). In a full circle are 2pi radians. So the length of intercepted arc from a central angle with measure 2pi is 2(pi)(r).

Length of arc = angle (in radians)*radius = (pi/4)*14 = 10.996 cm

A central angle is measured by its intercepted arc. Let's denote the length of the intercepted arc with s, and the length of the radius r. So, s = 6 cm and r = 30 cm. When a central angle intercepts an arc whose length measure equals the length measure of the radius of the circle, this central angle has a measure 1 radian. To find the angle in our problem we use the following relationship: measure of an angle in radians = (length of the intercepted arc)/(length of the radius) measure of our angle = s/r = 6/30 = 1/5 radians. Now, we need to convert this measure angle in radians to degrees. Since pi radians = 180 degrees, then 1 radians = 180/pi degrees, so: 1/5 radians = (1/5)(180/pi) degrees = 36/pi degrees, or approximate to 11.5 degrees.

If the radius of a circle is tripled, how is the length of the arc intercepted by a fixed central angle changed?

-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees

We have a formula of finding the arc length, s = θr, where s is the length of the intercepted arc, θ is the central angle measured in radians, and r is the radius of the circle. So that we need to convert 50 degrees in radians. 1 degrees = pi/180 radians 50 degrees = 50(pi/180) radians = 5pi/18 radians s = θr (replace θ with 5pi/18, and r with 3.5) s = (5pi/18)(3.5) = (17.5/18) pi ≈ 3 Thus, the length of the arc is about 3.

The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.

arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.

Length of arc: 115/360 times (130pi) = 130.5 inches rounded

2pi/9 radians or 40 degrees

You can think of an arc as a fraction of the circumferance of a circle. Also, a complete circle is 2pi radians, so any central angle is THETA / 2pi of a complete circle. Multiply by the circumferance to get the length of the arc: THETA / 2pi * 2(pi)(r) = THETA * r or the length of the arc is simply the radius times the central angle in radians

An arc of length 6cm subtending an angle at the centre of 1.5c is equivalent to the whole circle of length 2πr subtending 2π radians. Therefore, 6/1.5 = 2πr/2π = r : Then r = 4 cm. NOTE : A radian can be defined as the angle at the centre of a circle subtended by an arc equal in length to the radius. So an arc subtending an angle of 2 radians is twice the length of the radius. An arc subtending an angle of 1.5 radians is thus 11/2 times as long as the radius.