Printable math worksheet for calculating area and circumference of circles.

To solve the problem of finding the exact area and circumference of each circle, we need to use the following formulas:

1. Circumference of a Circle:
\[
C = 2\pi r \quad \text{or} \quad C = \pi d
\]
where \( r \) is the radius and \( d \) is the diameter.

2. Area of a Circle:
\[
A = \pi r^2
\]
where \( r \) is the radius.

Let's go through each circle step by step.

---

Circle 1:

- Diameter (\( d \)): 41 cm
- Radius (\( r \)):
\[
r = \frac{d}{2} = \frac{41}{2} = 20.5 \, \text{cm}
\]
- Circumference (\( C \)):
\[
C = \pi d = \pi \times 41 = 41\pi \, \text{cm}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (20.5)^2 = \pi \times 420.25 = 420.25\pi \, \text{cm}^2
\]

Summary for Circle 1:
- Radius: \( 20.5 \, \text{cm} \)
- Diameter: \( 41 \, \text{cm} \)
- Circumference: \( 41\pi \, \text{cm} \)
- Area: \( 420.25\pi \, \text{cm}^2 \)

---

Circle 2:

- Radius (\( r \)): 7 cm
- Diameter (\( d \)):
\[
d = 2r = 2 \times 7 = 14 \, \text{cm}
\]
- Circumference (\( C \)):
\[
C = 2\pi r = 2\pi \times 7 = 14\pi \, \text{cm}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (7)^2 = \pi \times 49 = 49\pi \, \text{cm}^2
\]

Summary for Circle 2:
- Radius: \( 7 \, \text{cm} \)
- Diameter: \( 14 \, \text{cm} \)
- Circumference: \( 14\pi \, \text{cm} \)
- Area: \( 49\pi \, \text{cm}^2 \)

---

Circle 3:

- Diameter (\( d \)): 18 m
- Radius (\( r \)):
\[
r = \frac{d}{2} = \frac{18}{2} = 9 \, \text{m}
\]
- Circumference (\( C \)):
\[
C = \pi d = \pi \times 18 = 18\pi \, \text{m}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (9)^2 = \pi \times 81 = 81\pi \, \text{m}^2
\]

Summary for Circle 3:
- Radius: \( 9 \, \text{m} \)
- Diameter: \( 18 \, \text{m} \)
- Circumference: \( 18\pi \, \text{m} \)
- Area: \( 81\pi \, \text{m}^2 \)

---

Circle 4:

- Radius (\( r \)): 9 in
- Diameter (\( d \)):
\[
d = 2r = 2 \times 9 = 18 \, \text{in}
\]
- Circumference (\( C \)):
\[
C = 2\pi r = 2\pi \times 9 = 18\pi \, \text{in}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (9)^2 = \pi \times 81 = 81\pi \, \text{in}^2
\]

Summary for Circle 4:
- Radius: \( 9 \, \text{in} \)
- Diameter: \( 18 \, \text{in} \)
- Circumference: \( 18\pi \, \text{in} \)
- Area: \( 81\pi \, \text{in}^2 \)

---

Circle 5:

- Diameter (\( d \)): 24 ft
- Radius (\( r \)):
\[
r = \frac{d}{2} = \frac{24}{2} = 12 \, \text{ft}
\]
- Circumference (\( C \)):
\[
C = \pi d = \pi \times 24 = 24\pi \, \text{ft}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (12)^2 = \pi \times 144 = 144\pi \, \text{ft}^2
\]

Summary for Circle 5:
- Radius: \( 12 \, \text{ft} \)
- Diameter: \( 24 \, \text{ft} \)
- Circumference: \( 24\pi \, \text{ft} \)
- Area: \( 144\pi \, \text{ft}^2 \)

---

Circle 6:

- Radius (\( r \)): 5 in
- Diameter (\( d \)):
\[
d = 2r = 2 \times 5 = 10 \, \text{in}
\]
- Circumference (\( C \)):
\[
C = 2\pi r = 2\pi \times 5 = 10\pi \, \text{in}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (5)^2 = \pi \times 25 = 25\pi \, \text{in}^2
\]

Summary for Circle 6:
- Radius: \( 5 \, \text{in} \)
- Diameter: \( 10 \, \text{in} \)
- Circumference: \( 10\pi \, \text{in} \)
- Area: \( 25\pi \, \text{in}^2 \)

---

Circle 7:

- Diameter (\( d \)): 30 mm
- Radius (\( r \)):
\[
r = \frac{d}{2} = \frac{30}{2} = 15 \, \text{mm}
\]
- Circumference (\( C \)):
\[
C = \pi d = \pi \times 30 = 30\pi \, \text{mm}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (15)^2 = \pi \times 225 = 225\pi \, \text{mm}^2
\]

Summary for Circle 7:
- Radius: \( 15 \, \text{mm} \)
- Diameter: \( 30 \, \text{mm} \)
- Circumference: \( 30\pi \, \text{mm} \)
- Area: \( 225\pi \, \text{mm}^2 \)

---

Circle 8:

- Radius (\( r \)): 6 cm
- Diameter (\( d \)):
\[
d = 2r = 2 \times 6 = 12 \, \text{cm}
\]
- Circumference (\( C \)):
\[
C = 2\pi r = 2\pi \times 6 = 12\pi \, \text{cm}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (6)^2 = \pi \times 36 = 36\pi \, \text{cm}^2
\]

Summary for Circle 8:
- Radius: \( 6 \, \text{cm} \)
- Diameter: \( 12 \, \text{cm} \)
- Circumference: \( 12\pi \, \text{cm} \)
- Area: \( 36\pi \, \text{cm}^2 \)

---

Circle 9:

- Diameter (\( d \)): 45 cm
- Radius (\( r \)):
\[
r = \frac{d}{2} = \frac{45}{2} = 22.5 \, \text{cm}
\]
- Circumference (\( C \)):
\[
C = \pi d = \pi \times 45 = 45\pi \, \text{cm}
\]
- Area (\( A \)):
\[
A = \pi r^2 = \pi (22.5)^2 = \pi \times 506.25 = 506.25\pi \, \text{cm}^2
\]

Summary for Circle 9:
- Radius: \( 22.5 \, \text{cm} \)
- Diameter: \( 45 \, \text{cm} \)
- Circumference: \( 45\pi \, \text{cm} \)
- Area: \( 506.25\pi \, \text{cm}^2 \)

---

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|c|}
\hline
\text{Circle} & \text{Radius} & \text{Diameter} & \text{Circumference} & \text{Area} \\
\hline
1 & 20.5 \, \text{cm} & 41 \, \text{cm} & 41\pi \, \text{cm} & 420.25\pi \, \text{cm}^2 \\
2 & 7 \, \text{cm} & 14 \, \text{cm} & 14\pi \, \text{cm} & 49\pi \, \text{cm}^2 \\
3 & 9 \, \text{m} & 18 \, \text{m} & 18\pi \, \text{m} & 81\pi \, \text{m}^2 \\
4 & 9 \, \text{in} & 18 \, \text{in} & 18\pi \, \text{in} & 81\pi \, \text{in}^2 \\
5 & 12 \, \text{ft} & 24 \, \text{ft} & 24\pi \, \text{ft} & 144\pi \, \text{ft}^2 \\
6 & 5 \, \text{in} & 10 \, \text{in} & 10\pi \, \text{in} & 25\pi \, \text{in}^2 \\
7 & 15 \, \text{mm} & 30 \, \text{mm} & 30\pi \, \text{mm} & 225\pi \, \text{mm}^2 \\
8 & 6 \, \text{cm} & 12 \, \text{cm} & 12\pi \, \text{cm} & 36\pi \, \text{cm}^2 \\
9 & 22.5 \, \text{cm} & 45 \, \text{cm} & 45\pi \, \text{cm} & 506.25\pi \, \text{cm}^2 \\
\hline
\end{array}
}
\]