Independent practice worksheet for calculating the area and circumference of circles, featuring real-world word problems.

Problem Analysis and Solutions

The worksheet involves solving problems related to the area and circumference of a circle. We will solve each problem step by step.

---

#### Problem 1:
Mike purchases a round wall clock. The clock’s radius is 10 m. What is the circumference of the clock?

- Formula for Circumference:
\[
C = 2\pi r
\]
where \( r \) is the radius.

- Given:
\( r = 10 \, \text{m} \)

- Solution:
\[
C = 2\pi \times 10 = 20\pi \, \text{m}
\]

Using \( \pi \approx 3.14 \):
\[
C \approx 20 \times 3.14 = 62.8 \, \text{m}
\]

- Answer:
\[
\boxed{62.8 \, \text{m}}
\]

---

#### Problem 2:
Jordan buys a drum. The diameter of a drum is 12 feet. What is the area of the drum?

- Formula for Area:
\[
A = \pi r^2
\]
where \( r \) is the radius.

- Given:
Diameter \( d = 12 \, \text{ft} \).
Radius \( r = \frac{d}{2} = \frac{12}{2} = 6 \, \text{ft} \).

- Solution:
\[
A = \pi r^2 = \pi (6)^2 = 36\pi \, \text{ft}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 36 \times 3.14 = 113.04 \, \text{ft}^2
\]

- Answer:
\[
\boxed{113.04 \, \text{ft}^2}
\]

---

#### Problem 3:
Hannah wants to make a plate for her mother. The radius of the plate is 1 foot. What is the plate’s circumference?

- Formula for Circumference:
\[
C = 2\pi r
\]

- Given:
\( r = 1 \, \text{ft} \)

- Solution:
\[
C = 2\pi \times 1 = 2\pi \, \text{ft}
\]

Using \( \pi \approx 3.14 \):
\[
C \approx 2 \times 3.14 = 6.28 \, \text{ft}
\]

- Answer:
\[
\boxed{6.28 \, \text{ft}}
\]

---

#### Problem 4:
Bobby made cookies. The circumferences of cookies are 6 cm. What is the diameter of the cookies?

- Formula for Circumference:
\[
C = \pi d
\]
where \( d \) is the diameter.

- Given:
\( C = 6 \, \text{cm} \)

- Solution:
Rearrange the formula to solve for \( d \):
\[
d = \frac{C}{\pi} = \frac{6}{\pi}
\]

Using \( \pi \approx 3.14 \):
\[
d \approx \frac{6}{3.14} \approx 1.91 \, \text{cm}
\]

- Answer:
\[
\boxed{1.91 \, \text{cm}}
\]

---

#### Problem 5:
Timothy makes a round chocolate cake. He wants to put a cream layer on top. If the cake is 10 cm in diameter, how many square centimeters of cream layer does he need to put on the chocolate cake?

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
Diameter \( d = 10 \, \text{cm} \).
Radius \( r = \frac{d}{2} = \frac{10}{2} = 5 \, \text{cm} \).

- Solution:
\[
A = \pi r^2 = \pi (5)^2 = 25\pi \, \text{cm}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 25 \times 3.14 = 78.5 \, \text{cm}^2
\]

- Answer:
\[
\boxed{78.5 \, \text{cm}^2}
\]

---

#### Problem 6:
Pamela wants to buy a new Mercedes. The Mercedes wheel has a radius of 35". What is the area of the Mercedes wheel?

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
\( r = 35 \, \text{in} \)

- Solution:
\[
A = \pi r^2 = \pi (35)^2 = 1225\pi \, \text{in}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 1225 \times 3.14 = 3846.5 \, \text{in}^2
\]

- Answer:
\[
\boxed{3846.5 \, \text{in}^2}
\]

---

#### Problem 7:
Angela goes to the garden. There is a fountain. A circular fountain with a 10 m radius lies alone in the center of a circular park with a 200 m radius. Calculate the total walking area available to the park visitors.

- Total Walking Area:
This is the area of the park minus the area of the fountain.

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
- Radius of the park \( R = 200 \, \text{m} \)
- Radius of the fountain \( r = 10 \, \text{m} \)

- Solution:
1. Area of the park:
\[
A_{\text{park}} = \pi R^2 = \pi (200)^2 = 40000\pi \, \text{m}^2
\]

2. Area of the fountain:
\[
A_{\text{fountain}} = \pi r^2 = \pi (10)^2 = 100\pi \, \text{m}^2
\]

3. Total walking area:
\[
A_{\text{walking}} = A_{\text{park}} - A_{\text{fountain}} = 40000\pi - 100\pi = 39900\pi \, \text{m}^2
\]

Using \( \pi \approx 3.14 \):
\[
A_{\text{walking}} \approx 39900 \times 3.14 = 125386 \, \text{m}^2
\]

- Answer:
\[
\boxed{125386 \, \text{m}^2}
\]

---

#### Problem 8:
Mary has a circular fountain in her garden. She wants to put a rope around it. The diameter of the fountain is 16 meters and diameter of the rope is 2 meters. What is the area of the fountain?

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
Diameter of the fountain \( d = 16 \, \text{m} \).
Radius of the fountain \( r = \frac{d}{2} = \frac{16}{2} = 8 \, \text{m} \).

- Solution:
\[
A = \pi r^2 = \pi (8)^2 = 64\pi \, \text{m}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 64 \times 3.14 = 200.96 \, \text{m}^2
\]

- Answer:
\[
\boxed{200.96 \, \text{m}^2}
\]

---

#### Problem 9:
A horse is tied with a rope in the center of grassland. The length of the rope is 50m. Find the area where the horse can graze.

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
Length of the rope \( r = 50 \, \text{m} \).

- Solution:
\[
A = \pi r^2 = \pi (50)^2 = 2500\pi \, \text{m}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 2500 \times 3.14 = 7850 \, \text{m}^2
\]

- Answer:
\[
\boxed{7850 \, \text{m}^2}
\]

---

#### Problem 10:
Lori made a round cookie cake. The diameter of the cake is 8 cm. What is the area of the cake?

- Formula for Area:
\[
A = \pi r^2
\]

- Given:
Diameter \( d = 8 \, \text{cm} \).
Radius \( r = \frac{d}{2} = \frac{8}{2} = 4 \, \text{cm} \).

- Solution:
\[
A = \pi r^2 = \pi (4)^2 = 16\pi \, \text{cm}^2
\]

Using \( \pi \approx 3.14 \):
\[
A \approx 16 \times 3.14 = 50.24 \, \text{cm}^2
\]

- Answer:
\[
\boxed{50.24 \, \text{cm}^2}
\]

---

Final Answers:

1. \(\boxed{62.8 \, \text{m}}\)
2. \(\boxed{113.04 \, \text{ft}^2}\)
3. \(\boxed{6.28 \, \text{ft}}\)
4. \(\boxed{1.91 \, \text{cm}}\)
5. \(\boxed{78.5 \, \text{cm}^2}\)
6. \(\boxed{3846.5 \, \text{in}^2}\)
7. \(\boxed{125386 \, \text{m}^2}\)
8. \(\boxed{200.96 \, \text{m}^2}\)
9. \(\boxed{7850 \, \text{m}^2}\)
10. \(\boxed{50.24 \, \text{cm}^2}\)