# Thread: finding area of a circular sector

1. ## finding area of a circular sector

Hello all! I just found this site and was hoping I could get some Trig help.

Could you please check my work?

given r=9cm and theta=120deg

$\displaystyle A=1/2(r^2)(/theta)$

$\displaystyle 1/2(9cm)^2(120/360)$

$\displaystyle 1/2(81cm^2)(120/360)$

$\displaystyle (40.5cm^2)(120/360)$

$\displaystyle A=13.5cm^2$

Thanks for taking a look!

Joe

2. Not quite. Change 120 degrees into radians, and don't divide by 360. I think you are still thinking in terms of the sector being a ratio [fraction] of the entire circle, but that was done in developing the formula in the first place. Once you have the formula, and you do, just plug and chug, but DO use radians, not degrees.

3. $\displaystyle A=1/2(r^2)(/theta)$

$\displaystyle 1/2(9cm)^2(120pi/180)$

$\displaystyle 1/2(81cm^2)(2pi/3)$

$\displaystyle (40.5cm^2)(2pi/3)$ <------ this is where I get stuck. Am I supposed to convert this to decimal form?

$\displaystyle (40.5cm^2)(.1960)$

$\displaystyle A=7.9398cm^2$

4. Originally Posted by rasczak
$\displaystyle A=1/2(r^2)(/theta)$

$\displaystyle 1/2(9cm)^2(120pi/180)$

$\displaystyle 1/2(81cm^2)(2pi/3)$

$\displaystyle (40.5cm^2)(2pi/3)$ <------ this is where I get stuck. Am I supposed to convert this to decimal form? Mr F says: It depends on whether the question requires an exact answer or an approximate answer. Note that this answer can be further simplified.

$\displaystyle (40.5cm^2)(.1960)$

$\displaystyle A=7.9398cm^2$
..

5. Originally Posted by mr fantastic
..
The original question was

a.) Find the length of the arc of the colored sector
b.) Find the area of the sector.