A circle has a radius of 4 m. What is the length of an arc that subtends a centr

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Question: A circle has a radius of 4 m. What is the length of an arc that subtends a central angle of 90 degrees?

Options:

Correct Answer: π/2 m

Solution:

Arc length = (θ/360) * 2πr; θ = 90; Arc length = (90/360) * 2π(4) = π/2 m.

A circle has a radius of 4 m. What is the length of an arc that subtends a central angle of 90 degrees?

A circle has a radius of 4 m. What is the length of an arc that subtends a central angle of 90 degrees?

Step 1: Identify the radius of the circle, which is given as 4 meters.
Step 2: Identify the central angle in degrees, which is given as 90 degrees.
Step 3: Use the formula for arc length: Arc length = (θ/360) * 2πr.
Step 4: Substitute the values into the formula: Arc length = (90/360) * 2π(4).
Step 5: Simplify the fraction 90/360 to get 1/4.
Step 6: Calculate 2π(4) to get 8π.
Step 7: Multiply 1/4 by 8π to get 2π.
Step 8: The final answer for the arc length is 2π/4, which simplifies to π/2 meters.

Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the central angle in degrees.
Understanding Central Angles – Recognizing how the central angle relates to the fraction of the circle represented by the arc.