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.
