Question

question 3 of 10
if r is the radius of a circle and d is its diameter, which of the following is an equivalent formula for the circumference c = 2πr?
a. c = 2πd
b. c = 2πd²
c. c = 2πrd
d. c = πd

Explanation:

Step1: Recall the relationship between radius and diameter

The diameter \(d\) of a circle is related to the radius \(r\) by the formula \(d = 2r\).

Step2: Substitute \(r=\frac{d}{2}\) into the circumference formula \(C = 2\pi r\)

Substitute \(r\) in \(C = 2\pi r\) with \(\frac{d}{2}\). So \(C=2\pi\times\frac{d}{2}\).
Simplify the expression \(2\pi\times\frac{d}{2}\). The \(2\) in the numerator and denominator cancels out, and we get \(C=\pi d\).

Answer:

D. \(C = \pi d\)