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The circumference of a circle is 15 pie centimeters. What is the area of the circle in terms of pie?

 Mar 20, 2020
 #1
avatar+22085 
+1

Circumference = pi * d    where d = diameter

 

circumference/pi = d      

circumference/2pi  = radius

 

Area = pi r^2   = pi   *( circumference/2pi)^2

                       = pi ( 15pi/2pi)^2

                       = pi * (15/2)^2    = 225/4  pi =56.25 pi  cm2

 Mar 20, 2020
 #2
avatar+402 
+1

This is kind of nitpicky but "pie" is not correct mathematically speaking; that's the food pie(the one that you eat). The correct way to spell it mathematically is "pi" but that's just something on the side. Getting to the problem at hand:

 

the circumference given is 15pi centimeters. The definition of the circumference of a circle is equal to: 2pi * r , with r being the radius. If we use that in the context of our problem, that gives us:

 

2 * pi * r = 15 * pi. Dividing by pi on both sides, we get:

2r = 15

r = 15/2

Now that we have our radius, we can find the area. The area of a circle is equal to: pi * r^2

 

Since we already have the radius, the area of the circle is equal to:

 

pi * (15/2)^2, which expands out to:

 

225/4 * pi

 Mar 20, 2020

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