What is the length of an arc of a circle with a radius of 4 cm that subtends an

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Question: What is the length of an arc of a circle with a radius of 4 cm that subtends an angle of 90° at the center?

Options:

Correct Answer: 2π cm

Solution:

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

What is the length of an arc of a circle with a radius of 4 cm that subtends an angle of 90° at the center?

What is the length of an arc of a circle with a radius of 4 cm that subtends an angle of 90° at the center?

Step 1: Identify the radius of the circle, which is given as 4 cm.
Step 2: Identify the angle subtended at the center of the circle, which is given as 90°.
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: Conclude that the length of the arc is 2π cm.

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