Question

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What is the area of the sector in the circle shown below?

Answer 1

\(\textit{sector of a circle}=\cfrac{\theta \pi r^2}{360}\qquad
\begin{cases}
r\to radius\\
\theta\to \textit{angle, in degrees}
\end{cases}\)

Answer 2

can you help me break this down? @jdoe0001

Answer 3

hmmm well.. check what your "radius" is
and check your angle

then just plug and chug

Answer 4

I got 3749.38?

Answer 5

@jdoe0001

Answer 6

hmmm need to check your PEMDAS

notice, \(\textit{sector of a circle}=\cfrac{\theta \pi r^2}{360}\qquad
\begin{cases}
r\to radius\to &10\\
\theta\to \textit{angle, in degrees}\to &37
\end{cases}
\\ \quad \\
\cfrac{37\cdot \pi \cdot 10^2}{360}\implies ?\)

Answer 7

32.27?

Answer 8

yes

Answer 9

\(32.27 in^2\) that is

Answer 10

thanks! could you help me with another? @jdoe0001

An angle measure of 82 degrees is equivalent to ____ radians. Round your answer to the nearest hundredth when necessary.

Answer 11

ok.. well.. how many say.... degrees in \(\pi\) radians?

Answer 12

3.14?

Answer 13

I have no idea, Im really bad at math

Answer 14

\(\large \pi = 3.14^o?\)

Answer 15

yes?

Answer 16

@jdoe0001

Answer 17

would it be 82/3.14? im so confused

Answer 18

hmmm nope... well. check your Unit Circle, see how many degrees are in a \(\large \pi\) firstly

Answer 19

180?

Answer 20

http://www.shelovesmath.com/wp-content/uploads/2012/11/Unit-Circle1.png <--- notice this Unit Circle

so... hmm yes 180

Answer 21

ok

Answer 22

\(\begin{array}{ccllll}
degrees&radians
\\\hline\\
180&\pi \\
82&x
\end{array}\implies \cfrac{180}{82}=\cfrac{\pi }{x}\implies x=\cfrac{82\cdot \pi }{180}\)

Answer 23

anyhow, "x" is how many degrees are in 82 :)

Answer 24

or rather, how many radians are in 82 degrees

Answer 25

1.43116999 radians?

Answer 26

is that the answer?

Answer 27

@jdoe0001

Answer 28

yeap

Answer 29

if I recall correctly, 1 radian is about 51 degrees
so 82 is about 1.4, sure

Answer 30

thanks!