What is the area of a circular region whose diameter is 6 centimeters? A \( 6 \pi \mathrm{~cm} \) B \( 9 \pi \mathrm{~cm} \) C \( 12 \pi \) square cm (D) \( 9 \pi \) square cm

To find the area of a circular region, we use the formula \( A = \pi r^2 \), where \( r \) is the radius. Since the diameter is 6 centimeters, the radius is half of that, which is 3 centimeters. Plugging this into the formula, we get \( A = \pi (3)^2 = 9\pi \) square centimeters. So, the correct answer is D \( 9 \pi \) square cm. Did you know that the concept of a circle goes back to ancient civilizations? The Egyptians used circular shapes in their architectural designs over 4,500 years ago! They recognized the importance of circular geometry, which has influenced how we build structures today. Circles aren't just math problems; they pop up everywhere in real life! From the wheels on your bike to the ripples formed when you throw a stone in water, understanding circles helps us in design, engineering, and even art. Embracing circles can add beauty, efficiency, and functionality to our inventions!