If a circle has a radius of 10 cm, what is the length of an arc that subtends a

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Question: If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 90 degrees?

Options:

Correct Answer: 17.5 cm

Solution:

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (90/360) * 2π(10) = 17.5 cm.

If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 90 degrees?

If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 90 degrees?

Step 1: Understand that the radius of the circle is 10 cm.
Step 2: Know that the central angle given is 90 degrees.
Step 3: Recall the formula for the length of an arc: L = (θ/360) * 2πr.
Step 4: Substitute the values into the formula: L = (90/360) * 2π(10).
Step 5: Simplify the fraction 90/360 to get 1/4.
Step 6: Calculate 2π(10) which equals 20π.
Step 7: Now multiply (1/4) by 20π to get 5π.
Step 8: Use the approximate value of π (about 3.14) to find the length: 5 * 3.14 = 15.7 cm.
Step 9: Therefore, the length of the arc is approximately 15.7 cm.

Arc Length Calculation – Understanding how to calculate the length of an arc using the formula L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.
Circle Properties – Knowledge of the properties of circles, including the relationship between radius, diameter, and circumference.