Question

The area of the sector wit hthe central angle a=120 degrees radians is equal to 24 square neters . how do i find the radius of the circle?

Answer 1

please help

Answer 2

degrees radians? Which is it?

Answer 3

Like this?

Answer 4

I would think we'd use the following equations:\[\Large
\frac{120^\circ}{360^\circ}=\frac{24m^2}{A}
\]\[\Large
A = \pi r^2
\]

Answer 5

So I would first solve for A, then solve for r. The second equation is just the equation for the area of a circle. The first equation is just using the fact that the angle is proportional to the area of the sector.

Answer 6

its 120 degrees

Answer 7

so how do i solve to get the radius

Answer 8

First find the area.

Answer 9

120/360 pie r 2

Answer 10

area us approx 603.18

Answer 11

Nope! Solve for A in the first equation.

Answer 12

It's going to be a round number

Answer 13

i dont have r though?

Answer 14

is A= pir r squared

Answer 15

Use \[\Large
\frac{120^\circ}{360^\circ}=\frac{24m^2}{A}\]

Answer 16

Cross multiply.

Answer 17

no clue

Answer 18

how can you cross multuiply that?

Answer 19

\[120^\circ \times A=360^\circ \times 24m^2\]

Answer 20

Then divide both sides by \[120 ^\circ \]

Answer 21

ohhh kk

Answer 22

a=3 * 24m2

Answer 23

can you walk me through the rest of the question?

Answer 24

Okay, so now we can use our second equation to find the radius\[ \large
A =3\times 24m^2 = 72m^2=\pi r^2 \text{ basically } 72m^2=\pi r^2
\]

Answer 25

So you need to solve for \(r\).

Answer 26

I'd start by dividing by \(\pi\)

Answer 27

Then you'd just take the square root of both sides so that \(r^2\) becomes \(r\).

Answer 28

what does the equation look like after i divide by pie

Answer 29

\[\large \frac{72}{\pi}m^2 = r^2\]

Answer 30

and then after i take the square root of both sides?