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

Guest Mar 20, 2020

#1**+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 cm^{2}

ElectricPavlov Mar 20, 2020

#2**+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**

jfan17 Mar 20, 2020