Question

eflect

1. what formula should be used to calculate the circumference of a circle if given the

circle’s diameter?

1. what formula should be used to calculate the circumference of a circle if given the

circle’s radius?

1. why are there two formulas for calculating the circumference of a circle?

Explanation:

Question 1

Step1: Recall circle circumference - diameter relation

The formula relating the circumference (\(C\)) and diameter (\(d\)) of a circle is based on the constant \(\pi\) (pi). The circumference is \(\pi\) times the diameter.
\(C = \pi d\)

Step1: Recall radius - diameter relation

We know that the diameter \(d\) of a circle is twice the radius \(r\) (\(d = 2r\)). Substitute this into the circumference - diameter formula.

Step2: Derive circumference - radius formula

From \(C=\pi d\) and \(d = 2r\), we substitute \(d\) to get \(C=\pi\times(2r)=2\pi r\).

The two formulas exist because the radius and diameter of a circle are related (\(d = 2r\)). One formula (\(C=\pi d\)) uses the diameter (the distance across the circle through its center), and the other (\(C = 2\pi r\)) uses the radius (the distance from the center to the edge). Depending on what measurement (diameter or radius) is given, we can use the corresponding formula for easier calculation. For example, if we know the radius, using \(C = 2\pi r\) is direct, and if we know the diameter, \(C=\pi d\) is direct, without needing to convert between them first.

Answer:

The formula is \(C=\pi d\) (where \(C\) is the circumference and \(d\) is the diameter of the circle).

Question 2