Question

What is the total perimeter of a semicircle whose radius is \( k \)?

• A. \( \pi k \)
• B. \( (\pi + 1) k \)
• C. \( \pi + 2k \)
• D. \( (\pi + 2) k \)

Hint:

For the perimeter of a semicircle, add half of the circumference and the diameter.

Answer 1

The Correct Option is D

The perimeter of a semicircle is the sum of the curved part (half of the circumference) and the diameter. The formula for the circumference of a full circle is \( 2 \pi r \), so the curved part of the semicircle is \( \pi r \). The diameter of the semicircle is \( 2r \). Thus, the total perimeter of the semicircle is: \[ \text{Perimeter} = \pi r + 2r = (\pi + 2) r. \] Since the radius is \( k \), the perimeter becomes: \[ \boxed{(\pi + 2) k}. \]