12 The total perimeter of a semicircle is 19.02 cm . Calculate the radius of the semicircle.

To find the radius of the semicircle, we can start by noting that the perimeter \( P \) of a semicircle is given by the formula: \[ P = \pi r + 2r \] where \( r \) is the radius and \( \pi \) is approximately 3.14. Given that the total perimeter is 19.02 cm, we can set up the equation: \[ \pi r + 2r = 19.02 \] Substituting \( \pi \) with 3.14, we have: \[ 3.14r + 2r = 19.02 \] Combining the terms gives: \[ 5.14r = 19.02 \] Now, divide both sides by 5.14: \[ r = \frac{19.02}{5.14} \approx 3.70 \] So, the radius of the semicircle is approximately 3.70 cm. To add a sprinkle of fun, did you know that semicircles are often associated with the beauty of arcs in nature and architecture? From the elegant arches of bridges to the smooth curve of a pizza slice, the shape is not just mathematically pleasing but also omnipresent in our world! Also, if you're curious about a real-world application, semicircles are often utilized in design and engineering. They can be found in structures, like the famous St. Louis Arch, which boasts a beautifully rounded shape, making it both a practical solution to creating large openings and a stunning visual landmark!