Question

Select all of the true statements:

pi is the circumference of a circle of radius 1
pi is the circumference of a circle of diameter 1
pi is the constant of proportionality relating the diameter of a circle to its circumference
pi is the constant of proportionality
a) 1, 3, 4
b) 2, 4
c) 3, 5
d) 1, 2, 5, 6

Answer 1

From the provided options, the correct answer is (b) 2, 4, because pi is the circumference of a circle with diameter 1 and is also the constant of proportionality relating the diameter of a circle to its circumference.

Step-by-step explanation:

The question we are addressing is which statements about π (pi) are true. Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. The statements provided are:

1. Pi is the circumference of a circle of radius 1
2. Pi is the circumference of a circle of diameter 1
3. Pi is the constant of proportionality relating the diameter of a circle to its circumference
4. Pi is the constant of proportionality

Statement 1 is incorrect because the circumference of a circle of radius 1 is 2π, not π. Statement 2 is correct; the circumference of a circle of diameter 1 is indeed π. Statement 3 is also correct; π is the constant of proportionality that relates the diameter of any circle to its circumference, whereby C = πd. Statement 4 is too vague without context; pi can be a constant of proportionality in the specific relationship between the diameter and circumference of a circle, but without more information, this statement is ambiguous. Hence, the correct statements are 2 and 3.

Therefore, the correct answer from the provided options is (b) 2, 4.