A circle has a radius of 5 cm. What is the length of an arc that subtends an ang

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Question: A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)

Options:

Correct Answer: 5.24 cm

Exam Year: 2023

Solution:

Arc length = (θ/360) × 2πr; = (60/360) × 2π × 5 ≈ 5.24 cm.

A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)

A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)

Step 1: Understand that the arc length formula is Arc length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.
Step 2: Identify the values given in the problem. The radius (r) is 5 cm and the angle (θ) is 60 degrees.
Step 3: Substitute the values into the formula: Arc length = (60/360) × 2π × 5.
Step 4: Simplify the fraction 60/360 to 1/6.
Step 5: Calculate 2π × 5, which equals 10π.
Step 6: Now multiply (1/6) by 10π: Arc length = (1/6) × 10π.
Step 7: Calculate the arc length: Arc length ≈ (1/6) × 31.42 (using π ≈ 3.14) ≈ 5.24 cm.

Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the angle in degrees.