C = 2\pi \times 5 = 10\pi
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- 5**Question:** An ornithologist observes a bird flying in a circular path with a radius of $5$ units. If the bird completes one full circle, compute the total distance traveled.
- Solution:** The distance traveled by the bird completing one full circle is the circumference of the circle. The formula for the circumference \(C\) of a circle is given by:
- where \(r\) is the radius. Substituting \(r = 5\), we get:
- Thus, the total distance traveled by the bird is \(\boxed{10\pi}\).
- Question:** An electrical engineer designs a triangular circuit board where the sides are \(7\) units, \(24\) units, and \(25\) units. Find the area of the triangle using Heron's formula.
- Solution:** To find the area of the triangle using Heron's formula, first compute the semi-perimeter \(s\):
