A circle has a radius of 5 cm. What is the length of an arc that subtends an ang

₹0.0

Question: A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)

Options:

Correct Answer: 5.24 cm

Exam Year: 2020

Solution:

Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.

A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)

A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)

Step 1: Identify the radius of the circle, which is given as 5 cm.
Step 2: Identify the angle subtended by the arc at the center, which is given as 60 degrees.
Step 3: Use the formula for arc length: Arc length = (θ/360) * 2πr.
Step 4: Substitute the values into the formula: Arc length = (60/360) * 2 * π * 5.
Step 5: Simplify the fraction 60/360 to 1/6.
Step 6: Calculate 2 * π * 5, which equals 10π.
Step 7: Multiply (1/6) by 10π to find the arc length: Arc length = (10π)/6.
Step 8: Simplify (10π)/6 to (5π)/3.
Step 9: Use a calculator to find the numerical value of (5π)/3, which is approximately 5.24 cm.

Arc Length Calculation – The formula for calculating the length of an arc based on the radius and the angle subtended at the center.
Understanding Degrees in Circle – Recognizing how to convert the angle in degrees to a fraction of the full circle (360 degrees) for calculations.