find, to the nearest tenth of an inch, the length of the arc intercepted by a central angle of (4pi)/3 radians if a radius of the circle is 22 inches long
C = 3.14D = 3.14(2*22) = 138.16 in. =
Circumference of circle.
L = 4pi/3*1/2pi * 138.16 = 92.1 in. =
Lengh of arc.
To find the length of an arc intercepted by a central angle, you can use the formula:
Arc Length = (Central Angle / 2π) x (2πr)
Given:
- Central angle: (4π)/3 radians
- Radius of the circle: 22 inches
1. Convert the central angle from radians to degrees:
Central Angle (in degrees) = (4π)/3 * (180/π) = (4/3) * 180 = 240 degrees
2. Substitute the values into the arc length formula:
Arc Length = (240 / 360) x (2π x 22)
3. Simplify the formula:
Arc Length = (2/3) x (2π x 22)
4. Calculate the arc length:
Arc Length ≈ (2/3) x (2 x 3.14159 x 22)
= (2/3) x (6.28318 x 22)
= (2/3) x (137.94616)
≈ 91.96411
Therefore, the length of the arc intercepted by a central angle of (4π)/3 radians is approximately 91.96411 inches, rounded to the nearest tenth of an inch.
To find the length of an arc intercepted by a central angle, you can use the formula:
Arc Length = (Angle / 2π) * 2πr
In this case, the given central angle is (4π)/3 radians, and the radius of the circle is 22 inches.
Let's plug the values into the formula:
Arc Length = ((4π)/3 / 2π) * 2π * 22
Simplifying:
Arc Length = (2/3) * 2π * 22
Arc Length = (4/3)π * 22
Arc Length ≈ 29.33 inches
Therefore, to the nearest tenth of an inch, the length of the arc intercepted by a central angle of (4π)/3 radians with a radius of 22 inches is approximately 29.3 inches.