An arc of a circle with radius of 14 cm subtends an angle of 135 degree at the centre. calculate the length of the arc
To calculate the length of an arc, you can use the formula:
\[ \text{{Length of arc}} = \frac{{\text{{angle in degrees}}}}{{360}} \times 2\pi r \]
Given:
Radius (r) = 14 cm
Angle (θ) = 135 degrees
By substituting the values into the formula:
Length of arc = \(\frac{{135}}{{360}} \times 2\pi \times 14\) cm
Simplifying the expression:
Length of arc = \(\frac{{3}}{{8}} \times \pi \times 14\) cm
Calculating the length of the arc:
Length of arc ≈ 16.54 cm (rounded to two decimal places)
Therefore, the length of the arc is approximately 16.54 cm.
To calculate the length of an arc of a circle, you need to know the radius of the circle and the angle that the arc subtends at the center.
In this case, the radius of the circle is given as 14 cm, and the angle subtended by the arc at the center is 135 degrees.
The formula to calculate the length of an arc is:
arc length = (angle / 360) * 2 * π * radius
Substituting the given values into the formula, we have:
arc length = (135 / 360) * 2 * π * 14
Simplifying the calculation:
arc length = (0.375) * 2 * 3.14 * 14
arc length ≈ 26.415 cm
Therefore, the length of the arc is approximately 26.415 cm.
c = 2 pi R
multiply that by 135/360