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:

The circumference of a circle is related to its radius \( r \) and diameter \( d \) (where \( d = 2r \)). The formula \( C = 2\pi r \) comes from substituting \( d = 2r \) into \( C=\pi d \), since \( d = 2r \), so \( C=\pi(2r)=2\pi r \). The formula \( C = \pi d \) is derived from the definition of \( \pi \) as the ratio of circumference to diameter (\( \frac{C}{d}=\pi \)), so multiplying both sides by \( d \) gives \( C = \pi d \). The other formulas: \( C=\pi r^{2} \) is the area of a circle, \( C = 2\pi d \) is incorrect (it would overstate the circumference), \( C=\pi d^{2} \) is incorrect (involves squaring the diameter, not related to circumference), and \( C=\pi r \) is incorrect (misses the factor of 2 when relating to radius).

Answer:

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