Question

find the radius and the diameter to the nearest hundredth when $c = 3\pi$ yd. use 3.14 for $\pi$.
the radius is \boxed{} yards.
the diameter is \boxed{} yards.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference \( C \) of a circle is \( C = \pi d \) (where \( d \) is the diameter) or \( C = 2\pi r \) (where \( r \) is the radius). We know \( C = 3\pi \) yd. First, let's find the diameter using \( C=\pi d \).
Substitute \( C = 3\pi \) into \( C=\pi d \): \( 3\pi=\pi d \). Divide both sides by \( \pi \) (since \( \pi
eq0 \)), we get \( d = 3 \) yd. Wait, but we can also use the numerical value of \( \pi = 3.14 \) to verify. Let's use \( C = 2\pi r \). Given \( C = 3\pi \), so \( 3\pi=2\pi r \). Divide both sides by \( \pi \), we get \( 3 = 2r \), then \( r=\frac{3}{2}=1.5 \) yd. Let's check with \( \pi = 3.14 \). \( C = 3\times3.14 = 9.42 \) yd. Using \( C = 2\pi r \), \( 9.42 = 2\times3.14\times r \). Then \( 9.42 = 6.28r \), so \( r=\frac{9.42}{6.28}=1.5 \) yd. And diameter \( d = 2r = 3.00 \) yd (to the nearest hundredth).

Step2: Confirm the values

Radius \( r = 1.50 \) yards (since 1.5 is already to the nearest hundredth, we can write it as 1.50), diameter \( d = 3.00 \) yards.

Answer:

The radius is \( \boldsymbol{1.50} \) yards.
The diameter is \( \boldsymbol{3.00} \) yards.