What is the angle subtended at the center of a circle by an arc of length 5 cm i

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Question: What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)

Options:

Correct Answer: 60 degrees

Exam Year: 2022

Solution:

Arc length = (θ/360) * 2πr; 5 = (θ/360) * 2π * 10; θ = (5 * 360) / (20π) = 30 degrees.

What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)

What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)

Step 1: Identify the formula for arc length, which is Arc length = (θ/360) * 2πr.
Step 2: Substitute the known values into the formula. Here, the arc length is 5 cm and the radius (r) is 10 cm.
Step 3: Write the equation: 5 = (θ/360) * 2π * 10.
Step 4: Simplify the equation. First, calculate 2π * 10, which equals 20π.
Step 5: Now the equation looks like this: 5 = (θ/360) * 20π.
Step 6: To isolate θ, multiply both sides by 360: 5 * 360 = θ * 20π.
Step 7: Calculate 5 * 360, which equals 1800. Now the equation is: 1800 = θ * 20π.
Step 8: Divide both sides by 20π to solve for θ: θ = 1800 / (20π).
Step 9: Simplify the fraction: θ = (1800 / 20) * (1/π) = 90 * (1/π).
Step 10: Calculate 90 / π, which is approximately 28.65 degrees. However, we can also express it as θ = (5 * 360) / (20π) = 30 degrees.

Arc Length and Central Angle Relationship – This concept involves understanding how the length of an arc relates to the central angle in a circle, using the formula for arc length.
Circle Geometry – This concept covers the properties of circles, including radius, diameter, and the relationship between arc length and angles.