A circle has a circumference of 42 inches. Using 3 to approximate pi, find the following: Diameter: \( \frac{14}{7} \frac{19}{90} \) Radius:

To find the diameter of a circle when its circumference is 42 inches, you can use the formula for circumference, \( C = \pi d \). By approximating \(\pi\) as 3, we can rearrange the formula: \[ d = \frac{C}{\pi} = \frac{42}{3} = 14 \text{ inches} \] Now, the radius \( r \) is half of the diameter, so: \[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ inches} \] Now, let's delve into some useful insights! The fascinating story of the circle dates back to ancient civilizations who studied its properties. The Egyptians and Babylonians, using their own rough versions of \(\pi\), contributed significantly to geometry. Fast forward to the Greeks, and mathematicians like Archimedes refined these calculations, helping establish the principles that underpin our understanding of circles today! Understanding circles is not just academic; it's practical! Whether you're embarking on DIY home projects, cooking with circular dishes, or biking around the park, knowing how to quickly find the radius and diameter helps you make better measurements. For instance, when laying out a garden bed, calculating the required space accurately ensures that your plants get the right conditions to flourish!