Question

which formulas can be used to find the circumference of a circle? choose all that apply. $c = pi d$ $c = 2pi r$ $c = 2pi d$ $c = pi d?$ $c = pi r^2$ $c = pi r$

Explanation:

Step1: Recall circle circumference formulas

The circumference \( C \) of a circle is related to its diameter \( d \) (where \( d = 2r \), \( r \) is radius) by the formulas: \( C=\pi d \) (since \( d = 2r \), substituting gives \( C = 2\pi r \)) and \( C = 2\pi r \). The formula \( C=\pi r^2 \) is for the area of a circle, \( C = 2\pi d \) is incorrect (as \( d = 2r \), so \( C=\pi d=2\pi r\), not \( 2\pi d \)), \( C=\pi r \) is incorrect, and \( C=\pi d^2 \) is incorrect. So the correct formulas are \( C = \pi d \) and \( C = 2\pi r \).

Step2: Identify correct options

From the given options, \( C=\pi d \) (first option) and \( C = 2\pi r \) (second option) are the correct formulas for the circumference of a circle. The other formulas either represent area (\( C=\pi r^2 \)) or are incorrect expressions for circumference.

Answer:

A. \( C = \pi d \)
B. \( C = 2\pi r \)