Question Video: Finding the Length of an Arc Given the Circle's Radius and the Measure of the Central Angle | Nagwa Question Video: Finding the Length of an Arc Given the Circle's Radius and the Measure of the Central Angle | Nagwa

Question Video: Finding the Length of an Arc Given the Circle's Radius and the Measure of the Central Angle Mathematics • First Year of Secondary School

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Find the length of the blue arc given the radius of the circle is 8 cm and the angle measure shown is in radians. Give the answer to one decimal place.

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Video Transcript

Find the length of the blue arc given the radius of the circle is eight centimeters and the angle measure shown is in radians. Give the answer to one decimal place.

In this question, we’re asked to find the length of the blue arc of the circle, which we will call 𝑙. We are told that the radius of the circle is eight centimeters. And the central angle is equal to four 𝜋 over three radians. We recall that the arc length 𝑙 for a circle with radius 𝑟 and a central angle of 𝜃 measured in radians is equal to the product of 𝑟 and 𝜃. This means that in our question 𝑙 is equal to eight multiplied by four 𝜋 over three. This is equal to 32𝜋 over three. Since we want the answer to one decimal place, we will type this into our calculator. 32𝜋 divided by three is equal to 33.5103 and so on. Rounding to one decimal place, we have 33.5. We can therefore conclude that the length of the blue arc is 33.5 centimeters to one decimal place.

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