What is the formula for the circumference of a semicircle?

What is the formula for the circumference of a semicircle?

• A. C = πr
• B. C = 2πr
• C. C = πd
• D. C = 2r

Answer: (A)

To determine the circumference of a semicircle, we start by understanding the full circumference formula for a circle, which is given by \( C = 2\pi r \), where \( r \) is the radius of the circle. A semicircle is half of a circle, so we take half of the full circumference. This leads us to: \[ \text{Circumference of semicircle} = \frac{1}{2} \times 2\pi r = \pi r \] However, we must also include the straight edge of the semicircle, which adds an additional length equal to the diameter of the semicircle. The diameter \( d \) is twice the radius (\( d = 2r \)). So we add this straight length to our previous calculation: \[ \text{Circumference of semicircle} = \pi r + 2r \] This shows that the total length around the semicircle (the curved part plus the straight part) is represented as: \[ C = \pi r + 2r \] Thus, while the curved part is accurately described by \( C = \pi r \), the complete circumference of a semicircle includes both segments. However, if the question

To determine the circumference of a semicircle, we start by understanding the full circumference formula for a circle, which is given by ( C = 2\pi r ), where ( r ) is the radius of the circle. A semicircle is half of a circle, so we take half of the full circumference. This leads us to:

[ \text{Circumference of semicircle} = \frac{1}{2} \times 2\pi r = \pi r ]

However, we must also include the straight edge of the semicircle, which adds an additional length equal to the diameter of the semicircle. The diameter ( d ) is twice the radius (( d = 2r )). So we add this straight length to our previous calculation:

[ \text{Circumference of semicircle} = \pi r + 2r ]

This shows that the total length around the semicircle (the curved part plus the straight part) is represented as:

[ C = \pi r + 2r ]

Thus, while the curved part is accurately described by ( C = \pi r ), the complete circumference of a semicircle includes both segments. However, if the question