Calculate the arc length that subtends an angle of 55 degree at the centre of a circle with radius r = 5cm.
An arc length l of radius r and angle θ (in radian measure) is:
l = rθ
Convert the angle from degrees to radians. Multiply the radius by that measure.
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To calculate the arc length that subtends an angle at the center of a circle, we use the formula:
Arc Length = (angle / 360) * 2 * π * radius
In this case, the angle is given as 55 degrees, and the radius is given as 5 cm. Plugging these values into the formula, we can calculate the arc length:
Arc Length = (55 / 360) * 2 * π * 5
Now, let's calculate step by step:
Step 1: Calculate the ratio of the given angle to a full circle (360 degrees):
55 / 360 = 0.1528
Step 2: Multiply the ratio by 2 * π (the circumference of a full circle):
0.1528 * 2 * π ≈ 0.9599 * π
Step 3: Multiply the result by the radius:
0.9599 * π * 5 ≈ 15.066 cm
Therefore, the arc length that subtends an angle of 55 degrees at the center of a circle with a radius of 5 cm is approximately 15.066 cm.