We want to see which of the given statements about the number pi are true.
The correct options are: a, d, and e.
First, let's talk a little bit about the number pi.
The irrational number pi is defined as the quotient between a circle's circumference and its diameter.
So if we know that a circle has a diameter D, the circumference of that circle is given by:
C = pi*D
Now let's analyze each option to see which ones are true.
a) "Pi is the area of a circle of radius 1."
The area of a circle of radius R is given by:
A = pi*R^2
So if the radius of this circle is R = 1. we have:
A = pi*1^2 = pi
So the area of this circle is pi, thus the statement is true.
b) "Pi is the area of a circle of diameter 1."
The diameter is twice the radius, so the radius of this circle is 0.5, we know that pi is the area of a circle of radius 1, not a circle of radius 0.5, so this is false.
c) "Pi is the circumference of a circle of radius 1."
The circumference of a circle of radius R is given by:
C = pi*2*R
If the radius is equal to 1 we have R = 1, then:
C = pi*2*1 = 2*pi
The circumference of this circle is 2*pi, not pi, so this is false.
d) "Pi is the circumference of a circle of diameter 1."
We know that the circumference of a circle of diameter D is:
C = pi*D
So if D = 1, we have:
C = pi*1 = pi
So the circumference of this circle is equal to pi, thus, this statement is true.
e) "Pi is the constant of proportionality relating the diameter of a circle to its circumference."
A proportional relation is:
y = k*x
where k is the constant of proportionality.
The relation between the circumference is given by:
C = pi*D
So yes, pi is the constant of proportionality, this is true.
F) "Pi is the constant of proportionality relating the radius of a circle to its area."
The area equation is:
A = pi*R^2
note that the radius is squared, so this is not a proportional relation, then the statement is false.
Finally, we can conclude that the true statements are:
a, d, e.
If you want to learn more, you can read:
https://brainly.com/question/7135052
