In a circle, if the radius is 10 cm, what is the length of an arc that subtends

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Question: In a circle, if the radius is 10 cm, what is the length of an arc that subtends an angle of 60 degrees at the center?

Options:

Correct Answer: 10.47 cm

Solution:

The length of an arc is given by the formula L = (θ/360) * 2πr. Here, L = (60/360) * 2 * π * 10 = (1/6) * 20π = 10.47 cm.

In a circle, if the radius is 10 cm, what is the length of an arc that subtends an angle of 60 degrees at the center?

In a circle, if the radius is 10 cm, what is the length of an arc that subtends an angle of 60 degrees at the center?

Step 1: Identify the radius of the circle, which is given as 10 cm.
Step 2: Identify the angle subtended by the arc at the center, which is given as 60 degrees.
Step 3: Recall the formula for the length of an arc: L = (θ/360) * 2πr.
Step 4: Substitute the values into the formula: L = (60/360) * 2 * π * 10.
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2 * π * 10, which equals 20π.
Step 7: Multiply (1/6) by 20π to get (20π/6).
Step 8: Simplify (20π/6) to (10π/3).
Step 9: Use a calculator to find the approximate value of (10π/3), which is about 10.47 cm.

Arc Length Calculation – Understanding how to calculate the length of an arc using the formula L = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.
Circle Geometry – Knowledge of basic properties of circles, including the relationship between radius, diameter, and arc length.