Video: Finding the Length of the Arc given Its Central Angle’s Measure and Its Circle’s Radius

Find the length of the blue arc given the radius of the circle is 8 cm. Give the answer to one decimal place.

01:20

Video Transcript

Find the length of the blue arc given the radius of the circle is eight centimetres. Give the answer to one decimal place.

We can go ahead and label one of the radii as eight centimetres. This is also a radius, so it would also be eight centimetres. So arc length, for a circle with radius 𝑟 and a central angle of 𝜃, in radians the arc length 𝑆 equals the product of 𝑟 and 𝜃, where 𝑟 would be the radius and 𝜃 would be an angle, in radians not degrees.

So we know the radius is eight and we know that 𝜃 is equal to four 𝜋 thirds. So our arc length would be equal to eight centimetres times four 𝜋 thirds. So multiplying these together, we get about 33.51 centimetres. But since it says to round to one decimal place, we need to look at the one and decide if that will make five stay a five or round up to six. And since one is less than five, that means our five here will stay a five. So the length of the blue arc would be 33.5 centimetres.

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