What is the arc length of a circle that has a 7-centimeter radius and a central angle that is 40 degrees? Use 3.14 for π and round your answer to the nearest hundredth.

Question

arindameducationusc · Answer

theta=L/R

usukidoll · Answer

hmmm my textbook is like this though for arc length
$$s = \theta r $$

arindameducationusc · Answer

where L = arc legth and r radius...
Now I hope you can solve it....
if not, ask me

usukidoll · Answer

s - arc length
theta - the angle
r - radius

usukidoll · Answer

I think we need to convert 40 degrees to radians
$$40 \times \frac{\pi}{180} \rightarrow \frac{40 \pi}{180}$$

usukidoll · Answer

simplify that fraction first ^_^

arindameducationusc · Answer

Awesome @UsukiDoll  Good job..
@JayDelV just follow @UsukiDoll

usukidoll · Answer

or we can reduce later....
$$s = \theta r  \rightarrow s = \frac{40 \pi}{180} \times 7$$

jaydelv · Answer

I'm actually confused, sorry was eating.

usukidoll · Answer

you're looking for the arc length of a circle

The arc length of a circle formula is 
$$s = \theta r $$
where s - arc length
theta - the angle
r - radius

we are given the angle which is 40 degrees, but it looks like we have to convert to radians
so multiply 40 by $$\frac{\pi}{180} $$

$$\frac{40 \pi}{180}$$
this fraction is reducible. afterwards, multiply by 7 
and you have your s which is the arc length

usukidoll · Answer

you were given an angle in degree mode. We can't use degree mode for this formula, so conversion to radians is necessary

usukidoll · Answer

it's best to reduce that fraction first.. otherwise you will be stuck with an even bigger fraction to reduce.

usukidoll · Answer

$$s = \theta r \rightarrow s =\frac{40 \pi}{180} \times 7 \rightarrow s = \frac{280 \pi}{180}$$
now that's a monster fraction to be reduced.

usukidoll · Answer

what is 280 divided by 10
what is 180 divided by 10

jaydelv · Answer

28 and 18

usukidoll · Answer

ok.. we still need to reduce further
$$s= \frac{28 \pi}{18}$$
but this time by 2

what is 28 divided by 2
what is 18 divided by 2

jaydelv · Answer

14 and 9

usukidoll · Answer

yes so we have 
$$s= \frac{14 \pi}{9}$$
we can't reduce anymore, so we got our arc length ;)

jaydelv · Answer

Thank you so much for your time I really appreciate it!

jaydelv · Answer

Oh wait, the answers are in decimals.

usukidoll · Answer

ah no problem we can convert to decimals XD

usukidoll · Answer

$$s= \frac{14 \pi}{9} \rightarrow s =\frac{14(3.14)}{9} \rightarrow s =\frac{43.96}{9}$$
$$s=4.8844444444444444444444$$
the 4 after the second 8 is repeating, so it's considered a repeating decimal.

jaydelv · Answer

Thank you !