If a circle has a radius of 3 cm, what is the length of an arc that subtends a c

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Question: If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 90 degrees?

Options:

Correct Answer: 2.36 cm

Solution:

Arc length = (θ/360) * 2πr = (90/360) * 2π(3) = (1/4) * 6π = 4.71 cm.

If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 90 degrees?

If a circle has a radius of 3 cm, what is the length of an arc that subtends a central angle of 90 degrees?

Step 1: Identify the radius of the circle. In this case, the radius (r) is 3 cm.
Step 2: Identify the central angle in degrees. Here, the angle (θ) is 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(3).
Step 5: Simplify the fraction 90/360 to 1/4.
Step 6: Calculate 2π(3) which equals 6π.
Step 7: Multiply (1/4) by 6π to get (1/4) * 6π = 6π/4 = 3π.
Step 8: Use the approximate value of π (about 3.14) to find the length: 3 * 3.14 = 9.42 cm.
Step 9: Therefore, the length of the arc is approximately 9.42 cm.

Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the central angle in degrees.
Understanding of Degrees and Radians – Knowledge of how to convert angles and apply them in formulas.
Circle Geometry – Basic properties of circles, including radius and circumference.