An arc substend an angle of 105 degree at d centre of a circle of radius 6cm . find the length of the arc if pi 22/7
(105º / 360º) * 2 * 6 cm * 22/7
What is the answer for the first one
To find the length of the arc, we need to use the formula:
Arc length = (θ/360) x 2πr
Where:
- θ is the angle in degrees,
- r is the radius of the circle.
Given that the angle θ is 105 degrees and the radius r is 6 cm, we can substitute these values into the formula:
Arc length = (105/360) x 2 x (22/7) x 6
Simplifying this expression:
Arc length = (105/360) x 2 x (22/7) x 6
Arc length = (7/24) x (2 x 22/7) x 6
Arc length = (7/24) x (44/7) x 6
Arc length = (7/4) x 2 x 6
Arc length = (7/4) x 12
Arc length = 7 x 3
Arc length = 21 cm
Therefore, the length of the arc is 21 cm.
To find the length of an arc in a circle, you can use the formula:
Arc Length = (Angle / 360) x (2πr)
Where:
- Angle is the central angle in degrees
- r is the radius of the circle
- π (pi) is a mathematical constant, approximately equal to 3.14159
In this case, we are given that the angle is 105 degrees and the radius is 6 cm. The value of π is given as 22/7.
Using the formula, we can calculate the length of the arc:
Arc Length = (105 / 360) x (2 x (22/7) x 6)
Simplifying the equation:
Arc Length = (0.2917) x (133.71)
Arc Length ≈ 38.91 cm
Therefore, the length of the arc is approximately 38.91 cm.