Question

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

Explanation:

The formula for the circumference of a circle is related to its diameter (\(d\)) or radius (\(r\)). We know that \(d = 2r\) (diameter is twice the radius) and the ratio of circumference to diameter is \(\pi\) (\(\frac{C}{d}=\pi\)), so \(C=\pi d\). Substituting \(d = 2r\) into \(C=\pi d\) gives \(C = 2\pi r\). Let's analyze each option:

• \(C = 2\pi d\): Incorrect, because \(C=\pi d\) (or \(2\pi r\)), not \(2\pi d\).
• \(C=\pi r^{2}\): This is the formula for the area of a circle, not the circumference.
• \(C=\pi d^{2}\): Incorrect, as it has \(d^{2}\) which is not part of the circumference formula.
• \(C=\pi r\): Incorrect, the correct formula with radius is \(C = 2\pi r\), not \(\pi r\).
• \(C = 2\pi r\): Correct, since \(d = 2r\), substituting into \(C=\pi d\) gives \(C = 2\pi r\).
• \(C=\pi d\): Correct, from the definition \(\frac{C}{d}=\pi\), so \(C=\pi d\).

Answer:

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