Formula for the perimeter of a semicircle
Understand the Problem
The question is asking for the mathematical formula used to calculate the perimeter (or circumference) of a semicircle, which includes both the curved part and the diameter.
Answer
$ \pi r + 2r $
Answer for screen readers
The perimeter of a semicircle is given by the formula $ \pi r + 2r $, where $r$ is the radius of the circle.
Steps to Solve
- Understand the components of the semicircle perimeter
The perimeter of a semicircle consists of the curved part (half of the circumference of a full circle) and the diameter.
- Calculate the circumference of the full circle
The circumference of a full circle is given by the formula:
$$ C = 2 \pi r $$
where $r$ is the radius of the circle.
- Calculate the curved part of the semicircle
Since the semicircle is half of the full circle, the curved part is:
$$ \text{Curved part} = \frac{1}{2} \times 2 \pi r = \pi r $$
- Add the diameter to the curved part
The diameter of the circle is twice the radius, given by:
$$ D = 2r $$
Therefore, the perimeter of the semicircle is:
$$ \text{Perimeter} = \pi r + 2r $$
The perimeter of a semicircle is given by the formula $ \pi r + 2r $, where $r$ is the radius of the circle.
More Information
The formula for the perimeter of a semicircle includes both the curved part and the diameter. It combines half the circumference of the circle and the diameter.
Tips
A common mistake is to forget to include the diameter when calculating the perimeter of the semicircle.