SOLUTION: Hi. I really can't understand this thing. It says "Find the area of each sector. Round your answers to the nearest tenth" The given is 'r = 10 mi, (theta) = pi/2' It's question num

Algebra ->  Trigonometry-basics -> SOLUTION: Hi. I really can't understand this thing. It says "Find the area of each sector. Round your answers to the nearest tenth" The given is 'r = 10 mi, (theta) = pi/2' It's question num      Log On


   

Question 631700: Hi. I really can't understand this thing. It says "Find the area of each sector. Round your answers to the nearest tenth" The given is 'r = 10 mi, (theta) = pi/2' It's question number 9 in my homework. Please help me, thank you so much! I need a reply ASAP.
Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
area of a circle is equal to pi*r^2.
area of a sector is equal to x/360 * the area of the circle.
this is equal to x/360- * pi*r^2.
x is equal to the number of degrees in the sector.
a sector is the area formed by the central angles and the arc formed on the circumference of the circle.
your angle is equal to pi/2.
this is the measure of your angle in radians.
to convert from radians to degrees, you have to multiply the radians by 180 / pi.
pi / 2 * 180 / pi = (pi * 180) / (2 * pi) = 180/2 = 90 degrees.
the radius of the circle is equal to 10 (given).
pi is always equal to 3.141592654
bottom line is:
the area of your sector is equal to:
90/360 * pi*r^2 which is equal to:
1/4 * pi*(10^2) which is equal to:
1/4 * pi*100 which is equal to:
78.53981634 units.
the area of the circle is equal to pi*r^2 which is equal to 100*pi which is equal to 314.1592654.
the area of your sector is 1/4 times this which makes the area of your sector equal to 78.53981634
it all checks out.
a diagram of your circle and the sector in question is shown below:
$$$$



Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
'r = 10 mi, (theta) = pi/2' 
What this means is that we started with a circle of radius 10


 

Now we cut out a "piece of pie" having an angle of pi%2F2 radians.

[How much is pi%2F2 radians when converted to degrees? Answer: 90°]

So we will cut out a piece of pie with a right angle.  That of course
amounts to taking 1%2F4th of the circle:



The area of the whole circle is given by

              A = pir²
              A = pi(10)²
              A = 100pi

So 1%2F4 of 100pi is 25pi = 25(3.1416) = 78.54 rounded to 

78.5

However your teacher may have expected you to use the formula for the
area of a sector of a circle ("piece of pie"):

             A = expr%281%2F2%29%2Atheta%2Ar%5E2
             A = expr%281%2F2%29%2Aexpr%28pi%2F2%29%2A10%5E2
             A = expr%28pi%2F4%29*100
             A = 25pi
             A = 25(3.1416) = 78.54 rounded to 78.5


Do it whichever way you were taught.

Edwin