We will look at some application problems using sector area and arc length This first
page has 5 problems on it so we are going to run through these together.
A pie is cut into 6 equal pieces.
The arc length of one piece of pie is 5.4 cm.
What is the diameter of the pie?
So our strategy is to always draw a picture.
Let's start by drawing a picture of the pie and assume it is a circular pie.
Let's draw 6 equal pieces.
(Draws 6 equal pieces) If we have 360 degrees divided by into 6 pieces our central angle
is going to be 60 degrees.
This gives you an idea of what we are working with and we also know that because it is cut
into 6 pieces,each slice represents 1/6 of the circle.
What we will do is use a " Proportion Method" that we used earlier.
If you remember the proportion method it works like this.
We take the arc length and put it over the circumference and set it equal to
measure of the angle over 360 degrees.
So let's plug in what we know.
The arc length equals is 5.4 and we don't know circumference which will become x,and
angle measure equals 60 degrees.
Next we look at this and this fraction reduces down to 1/6, and we can cross product.1 times
x and 6 times 5.4 I will grab my calculator 6x5.4= 32.4 which equals my circumference.
Next we can work backwards to find the diameter.
Circumference = Diameter times Pi which is 32.4 So I will take 32.4 and divide it by
Pi and I get 10.31 and there you go,and that would be the diameter of the Pie If we wanted
to write a sentence The pie's diameter
is 10.31 centimeters.
That would be your answer in a sentence.