Question

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

Explanation:

Step1: Recall Circumference Formula

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 \( C = 2\pi r \). Also, since \( d=2r \), \( C=\pi d \) and \( C = 2\pi r \) are equivalent. Let's check each option:

• \( C=\pi r \): Incorrect, missing a factor of 2 (should be \( 2\pi r \) or \( \pi d \)).
• \( C=\pi d \): Correct, as circumference is \( \pi \) times diameter.
• \( C=\pi d^{2} \): Incorrect, this is related to area (area of circle is \( \pi r^{2}=\frac{\pi d^{2}}{4} \), not circumference).
• \( C = 2\pi r \): Correct, as circumference is \( 2\pi \) times radius.
• \( C=\pi r^{2} \): Incorrect, this is the area formula, not circumference.
• \( C = 2\pi d \): Incorrect, diameter is \( d \), so multiplying by \( 2\pi \) is wrong (should be \( \pi d \) or \( 2\pi r \)).

Answer:

B. \( C = \pi d \), D. \( C = 2\pi r \)