# Arc Length, and Area of a sector

• Oct 2nd 2009, 04:47 PM
Nismo
Arc Length, and Area of a sector
Hi i need soem help on doign a problem please! I actually asked this problem to the teacher and showed him my work if this was how to do the problem and he said yes its all correct so i input it in the computer at home and it said the answer was wrong! here is the problem.

An arc of length 3 feet is cut off by a central angle of π/2 radians. Find the area of the sector formed. (Round the answer to two decimal places.)

|
V
______ ft^2

So what i did was. since they gave me s=3 and r=pi/2 i did 3/(pi/2), and i get 1.909859317. and then this gives me theta. so then i put it in the 1/2(r)^2(theta) and get 2.35619449 then round that to 2.36 and it says im wrong o_0 help please! thxs!
• Oct 2nd 2009, 05:07 PM
skeeter
Quote:

Originally Posted by Nismo
Hi i need soem help on doign a problem please! I actually asked this problem to the teacher and showed him my work if this was how to do the problem and he said yes its all correct so i input it in the computer at home and it said the answer was wrong! here is the problem.

An arc of length 3 feet is cut off by a central angle of π/2 radians. Find the area of the sector formed. (Round the answer to two decimal places.)

|
V
______ ft^2

So what i did was. since they gave me s=3 and r=pi/2 i did 3/(pi/2), and i get 1.909859317. and then this gives me theta. so then i put it in the 1/2(r)^2(theta) and get 2.35619449 then round that to 2.36 and it says im wrong o_0 help please! thxs!

$A = \frac{1}{2}r^2 \theta$

$\frac{1}{2} \cdot \frac{36}{\pi^2} \cdot \frac{\pi}{2} = \frac{9}{\pi} \approx 2.86$
• Oct 2nd 2009, 05:11 PM
Nismo
how did u get 36/pi?
• Oct 2nd 2009, 05:18 PM
skeeter
Quote:

Originally Posted by Nismo
how did u get 36/pi?

first of all it was $\frac{36}{\pi^2}$ , which is $r^2$.

$s = r\theta$

$r = \frac{s}{\theta} = \frac{3}{\frac{\pi}{2}} = \frac{6}{\pi}
$

so ... what is $r^2$ ?
• Oct 3rd 2009, 04:37 PM
HallsofIvy
Quote:

Originally Posted by Nismo
Hi i need soem help on doign a problem please! I actually asked this problem to the teacher and showed him my work if this was how to do the problem and he said yes its all correct so i input it in the computer at home and it said the answer was wrong! here is the problem.

An arc of length 3 feet is cut off by a central angle of π/2 radians. Find the area of the sector formed. (Round the answer to two decimal places.)

|
V
______ ft^2

So what i did was. since they gave me s=3 and r=pi/2 i did 3/(pi/2), and i get 1.909859317. and then this gives me theta. so then i put it in the 1/2(r)^2(theta) and get 2.35619449 then round that to 2.36 and it says im wrong o_0 help please! thxs!

I must confess that the last paragraph mystifies me. How does one "do" 3/(pi/2)? What do "s" and "r" represent and why did you divide s by r?

Do you know that pi/2 (90 degrees) is 1/4 of a complete circle? Do you know that the circumference of a circle is 2pi r (r is the radius of the circle). Here you know that 1/4 of the circle has circumference 3, what is the circumference of the entire circle? What is the radius of that circle?

Do you know that the area of a circle is pi r^2? What would the area of a circle of this radius be? What is the area of 1/4 of that circle?
• Oct 4th 2009, 08:46 AM
Nismo
Quote:

Originally Posted by HallsofIvy
I must confess that the last paragraph mystifies me. How does one "do" 3/(pi/2)? What do "s" and "r" represent and why did you divide s by r?

Do you know that pi/2 (90 degrees) is 1/4 of a complete circle? Do you know that the circumference of a circle is 2pi r (r is the radius of the circle). Here you know that 1/4 of the circle has circumference 3, what is the circumference of the entire circle? What is the radius of that circle?

Do you know that the area of a circle is pi r^2? What would the area of a circle of this radius be? What is the area of 1/4 of that circle?

well this was my thinking. Since i know a= 1/2r^2theta. then since i was given radius omg -_- nvm i keep getting the radius and radian r mixed up..... but yeah ill keep going on though.. sincei thought they already gave me radius i was going to find theta so used the s=r*theta and then that got me theta and i pluged that in and wahla -_- but yeah r=radius not radian....