If the circumference of a circle is 11pi, what is the area in terms of pi?

Question

I don't quite understand this. Is pi supposed to be a variable, or do I actually calculate 3.14 into the problem. Based off of context, it is a variable, since we are doing expressions in class, but I'm not sure

Answer 1

Pi is a constant, it always has the same value of pi = 3.1415....it is more convenient to express it as the constant because there is an infinite number of non-repeating decimals in pi and so any decimal approximation you use will not give you its exact value. You are right in thinking it is similar to a variable, a constant is also a symbol used to refer to a number, however a constant does not change value within the context of a math problem, while a variable can.

 

For figuring out the area, it is important to know there are a few relationships between the radius, circumference, and area of a circle. More specifically, both the area and circumference can be expressed in terms of the radius of the circle and the constant pi.

 

C = 2 * pi * r

A = pi * r²

 

where C is the circumference of the circle, A is the area of the circle, and r is the radius of the circle.

 

In your problem, you are told the circumference is 11 pi; based on this you can figure out the radius and you can then use the radius to calculate the area.

 

11 * pi = 2 * pi * r

 

(cancel pi on both sides, divide by 2 and you end up with)

r = 5.5

(now plug this for r in the formula for area)

A = pi * 5.5² = 30.25 * pi

 

So the area we can also leave expressed in terms of pi...if this seems hard to understand just think of other numbers like 2 million or 30.25 million. If we can say the number 30.25 million or 30.25 tens why not also 30.25 pi? When we say 30.25 million it may be easier to understand because we can immediately imagine the 000,000 we are tacking on to the end of the number, but it is the same concept...with the pi on the end you can also imagine a multiplication but since there are all these decimals, why bother doing it instead of leaving it in a  cleaner looking form in this way?

Answer 2

C=(pi)*diameter

11(pi)=(pi)*diameter

diameter=11

the radius is half the diameter

radius=11/2=5.5

A=(pi)*r^2 is the formula for the area of a circle

A=(pi)*(5.5)^2

A=(pi)*30.25

A=30.25pi is the area in terms of pi