Question

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

Explanation:

Step1: Recall circle circumference formulas

The circumference \( C \) of a circle is related to its radius \( r \) and diameter \( d \) (where \( d = 2r \)). The correct formulas are derived from the relationship between radius, diameter, and the constant \( \pi \).

Step2: Analyze each formula

• \( C = 2\pi d \): Incorrect, because \( d = 2r \), so substituting gives \( C = 2\pi(2r)=4\pi r \), which is wrong.
• \( C = 2\pi r \): Correct, since the circumference is \( 2 \) times \( \pi \) times the radius.
• \( C = \pi r^2 \): This is the formula for the area of a circle, not circumference.
• \( C = \pi d^2 \): Incorrect, it's not a valid circumference formula (involves \( d^2 \), which is for area - like terms).
• \( C = \pi r \): Incorrect, it's missing the factor of \( 2 \) from the correct \( 2\pi r \).
• \( C = \pi d \): Correct, since \( d = 2r \), so \( C=\pi d=\pi(2r) = 2\pi r \), which matches the correct formula.

Answer:

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