Question

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

Explanation:

Step1: Recall circle circumference concepts

The circumference \( C \) of a circle is related to its radius \( r \) and diameter \( d \) (where \( d = 2r \)). The basic relationship is \( \frac{C}{d}=\pi \), so \( C=\pi d \). Since \( d = 2r \), substituting \( d \) gives \( C = 2\pi r \).

Step2: Analyze each formula

• \( C=\pi r^{2} \): This is the area of a circle, not circumference.
• \( C = 2\pi r \): Valid, as \( d = 2r \), so \( C=\pi d=2\pi r \).
• \( C=\pi d^{2} \): Not a circumference formula (involves \( d^{2} \), like area with diameter).
• \( C = 2\pi d \): Incorrect, would be double the correct circumference.
• \( C=\pi r \): Incorrect, missing the factor of 2 from \( d = 2r \).
• \( C=\pi d \): Valid, from \( \frac{C}{d}=\pi \).

Answer:

\( C = 2\pi r \), \( C=\pi d \)