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 solve the problem, we start with the known condition that the circumference \( C \) of the circle is 42 inches. The formula for the circumference of a circle is given by: \[ C = \pi d \] where \( d \) is the diameter. We will use \( \pi \approx 3 \) for our calculations. ### Step 1: Calculate the Diameter Using the formula for circumference, we can rearrange it to find the diameter: \[ d = \frac{C}{\pi} \] Substituting the known values: \[ d = \frac{42}{3} = 14 \text{ inches} \] ### Step 2: Calculate the Radius The radius \( r \) of a circle is half of the diameter: \[ r = \frac{d}{2} \] Substituting the diameter we found: \[ r = \frac{14}{2} = 7 \text{ inches} \] ### Summary of Results - Diameter: \( 14 \) inches - Radius: \( 7 \) inches Now, let's also evaluate the expression given for the diameter: \[ \frac{14}{7} \cdot \frac{19}{90} \] Calculating this step-by-step: 1. Calculate \( \frac{14}{7} = 2 \). 2. Now calculate \( 2 \cdot \frac{19}{90} = \frac{38}{90} \). To simplify \( \frac{38}{90} \): \[ \frac{38 \div 2}{90 \div 2} = \frac{19}{45} \] Thus, the diameter expressed in the given form is \( \frac{19}{45} \). ### Final Results - Diameter: \( 14 \) inches (or \( \frac{19}{45} \) in the given form) - Radius: \( 7 \) inches