Find the length of an arc of a circle of radius 6cm which subtends an angle of 105 degree at the Centre of the circle
whole circumference = 12π
so your arc is 105/360 or 7/24 of that
To find the length of an arc of a circle, you can use the formula:
Arc length = (Angle/360) * (2 * π * radius)
Given:
Radius (r) = 6 cm
Angle (θ) = 105 degrees
Substituting the values into the formula:
Arc length = (105/360) * (2 * π * 6)
Simplifying:
Arc length = (7/24) * (12 * π)
Arc length = (7/2) * π
Therefore, the length of the arc is (7/2) * π cm.
To find the length of an arc of a circle, we can use the formula:
Arc Length = (Angle / 360) * (2 * π * Radius)
In this case, the radius of the circle is given as 6cm, and the angle subtended at the center of the circle is 105 degrees.
We can now substitute these values into the formula:
Arc Length = (105 / 360) * (2 * π * 6)
Simplifying further:
Arc Length = (0.2917) * (12 * π)
Arc Length ≈ 3.5 * π cm
So, the length of the arc is approximately 3.5 * π cm or 11 cm (rounding off to two decimal places).