\( C=18 \pi \) find the area in terms of pi

To find the area when the circumference \( C = 18\pi \), we first need to find the radius. The formula for the circumference of a circle is: \[ C = 2\pi r \] Setting \( 18\pi = 2\pi r \), we can solve for \( r \): \[ 18 = 2r \implies r = 9 \] Now, we can find the area \( A \) using the formula for the area of a circle: \[ A = \pi r^2 \] Substituting \( r = 9 \): \[ A = \pi (9^2) = \pi \times 81 = 81\pi \] Thus, the area in terms of pi is \( 81\pi \). But did you know that in ancient civilizations, people were already aware of the relationship between a circle's circumference and area? The Egyptians and Babylonians were using approximations of \( \pi \) to perform calculations related to fields and circular structures over 3,000 years ago! Their methods may not have had the precision we use today, but they laid the groundwork for geometry as we know it. Circles aren't just mathematical curiosities; they’re everywhere in our daily lives! From the wheels on your car to pizza sizes and even the shape of planets, circles play a crucial role in various fields. Engineers use circular designs for bridges, and artists utilize them for creating visually appealing compositions. Understanding the area and circumference of circles can help in practical scenarios, such as landscaping a circular garden or planning the layout of a circular pool, turning math into a tangible experience!