Worksheet for calculating the circumference of circles with real-world examples.

To solve the problems related to the circumference of a circle, we use the formula for the circumference of a circle:

\[
C = 2 \pi r
\]

where \( C \) is the circumference and \( r \) is the radius of the circle. If the diameter \( d \) is given instead of the radius, we can use the formula:

\[
C = \pi d
\]

Let's solve each problem step by step.

---

Problem 1:

A circular mirror has a radius of \( 1 \frac{1}{2} \) ft. Work out the circumference of the mirror.

#### Step 1: Identify the radius
The radius \( r \) is given as \( 1 \frac{1}{2} \) ft. Convert this mixed number to an improper fraction or decimal:
\[
1 \frac{1}{2} = 1.5 \text{ ft}
\]

#### Step 2: Use the formula for circumference
\[
C = 2 \pi r
\]
Substitute \( r = 1.5 \):
\[
C = 2 \pi (1.5)
\]
\[
C = 3 \pi
\]

#### Step 3: Approximate the value (if needed)
Using \( \pi \approx 3.14 \):
\[
C \approx 3 \times 3.14 = 9.42 \text{ ft}
\]

#### Final Answer:
\[
\boxed{9.4}
\]

---

Problem 2:

A tin of beans has a diameter of 3 inches. Work out the circumference of the top of the tin in terms of \( \pi \).

#### Step 1: Identify the diameter
The diameter \( d \) is given as 3 inches.

#### Step 2: Use the formula for circumference
\[
C = \pi d
\]
Substitute \( d = 3 \):
\[
C = \pi (3)
\]
\[
C = 3 \pi
\]

#### Final Answer:
\[
\boxed{3}
\]

---

Problem 3:

A circular plate has a radius of \( 5 \frac{1}{4} \) inches. What is the circumference of the plate?

#### Step 1: Identify the radius
The radius \( r \) is given as \( 5 \frac{1}{4} \) inches. Convert this mixed number to an improper fraction or decimal:
\[
5 \frac{1}{4} = 5.25 \text{ inches}
\]

#### Step 2: Use the formula for circumference
\[
C = 2 \pi r
\]
Substitute \( r = 5.25 \):
\[
C = 2 \pi (5.25)
\]
\[
C = 10.5 \pi
\]

#### Step 3: Approximate the value (if needed)
Using \( \pi \approx 3.14 \):
\[
C \approx 10.5 \times 3.14 = 32.97 \text{ inches}
\]

#### Final Answer:
\[
\boxed{33.0}
\]

---

Summary of Answers:

1. Circumference of the mirror: \(\boxed{9.4}\) ft
2. Circumference of the tin: \(\boxed{3}\) \(\pi\) inches
3. Circumference of the plate: \(\boxed{33.0}\) inches

---

Thus, the final boxed answers are:
\[
\boxed{9.4, 3, 33.0}
\]