Question

find the radius and the diameter to the nearest hundredth when c = π yd. use 3.14 for π.
the radius is

yard.
the diameter is

yard.

Explanation:

Step1: Recall 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 \( C=\pi \) yards (assuming the circumference is \( \pi \) yards, maybe a typo or misprint, but let's proceed with \( C = \pi \)) and \( \pi \approx 3.14 \). First, find the diameter using \( C=\pi d \).

Step2: Solve for Diameter

From \( C = \pi d \), we can solve for \( d \) by dividing both sides by \( \pi \): \( d=\frac{C}{\pi} \). Substituting \( C = \pi \) (assuming the circumference is \( \pi \) yards, maybe it's a unit or typo, but let's use \( C=\pi \)) and \( \pi = 3.14 \)? Wait, no—wait, maybe the circumference is \( C = \pi \) (like \( C = \pi \) yards, so \( C=\pi \)). Then \( d=\frac{C}{\pi}=\frac{\pi}{\pi}=1 \) yard? Wait, no, maybe the circumference is \( C = \pi \) (but the problem says "when \( C = \pi \) yd. Use 3.14 for \( \pi \)". Wait, that's confusing. Wait, maybe the circumference is \( C = \pi \) (so \( C=\pi \)), then:

Wait, let's correct: The formula \( C = \pi d \), so \( d=\frac{C}{\pi} \). If \( C = \pi \) (yards), then \( d = \frac{\pi}{\pi}=1 \) yard. Then radius \( r=\frac{d}{2}=\frac{1}{2}=0.5 \) yard. Wait, but maybe the circumference is \( C = \pi \) (like \( C = \pi \) yards, so using \( \pi = 3.14 \) is conflicting. Wait, no—maybe the circumference is \( C = \pi \) (so \( C=\pi \)), so:

Step3: Solve for Radius

Using \( C = 2\pi r \), we can solve for \( r \): \( r=\frac{C}{2\pi} \). If \( C = \pi \), then \( r=\frac{\pi}{2\pi}=\frac{1}{2}=0.5 \) yard. Then diameter \( d = 2r = 1 \) yard. Wait, but maybe the circumference is \( C = \pi \) (so \( C=\pi \)), so:

Wait, let's re-express. Let's assume the circumference \( C = \pi \) yards (maybe a typo, like \( C = \pi \) instead of a number). Then:

• Diameter \( d=\frac{C}{\pi}=\frac{\pi}{\pi}=1 \) yard.
• Radius \( r=\frac{d}{2}=\frac{1}{2}=0.5 \) yard.

But if the circumference was, say, \( C = \pi \) (like \( C = 3.14 \) yards? No, \( \pi \approx 3.14 \), so if \( C = \pi \), then \( d = 1 \), \( r = 0.5 \). Wait, maybe the problem has a typo, but let's proceed with \( C = \pi \) (circumference is \( \pi \) yards).

Wait, maybe the original problem has \( C = \pi \) (so circumference is \( \pi \) yards). Then:

Step1: Find Diameter

\( C = \pi d \implies d = \frac{C}{\pi} \). Substitute \( C = \pi \): \( d = \frac{\pi}{\pi} = 1 \) yard.

Step2: Find Radius

\( r = \frac{d}{2} = \frac{1}{2} = 0.5 \) yard.

But wait, if the circumference was \( C = \pi \) (like \( C = 3.14 \) yards? No, \( \pi \approx 3.14 \), so if \( C = 3.14 \) yards, then \( d = \frac{3.14}{3.14}=1 \) yard, \( r = 0.5 \) yard. So regardless, the diameter is 1 yard, radius is 0.5 yard.

Answer:

The radius is \( \boldsymbol{0.50} \) yard.
The diameter is \( \boldsymbol{1.00} \) yard.