Circumference and Area of Circles Worksheets - Free Printable

To solve the problems in the worksheet, we need to use the formulas for the area and circumference of a circle. Here are the relevant formulas:

1. Circumference of a Circle:
\[
C = 2\pi r
\]
where \( r \) is the radius of the circle.

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

We will solve each problem step by step.

---

Problem 1:

- Given: Radius \( r = 5 \) cm.
- Find: Circumference and Area.

#### Step 1: Calculate the Circumference
Using the formula \( C = 2\pi r \):
\[
C = 2\pi \times 5 = 10\pi \text{ cm}
\]

#### Step 2: Calculate the Area
Using the formula \( A = \pi r^2 \):
\[
A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ cm}^2
\]

#### Final Answer:
\[
\boxed{10\pi \text{ cm}, 25\pi \text{ cm}^2}
\]

---

Problem 2:

- Given: Diameter \( d = 14 \) cm.
- Find: Circumference and Area.

#### Step 1: Find the Radius
The radius \( r \) is half of the diameter:
\[
r = \frac{d}{2} = \frac{14}{2} = 7 \text{ cm}
\]

#### Step 2: Calculate the Circumference
Using the formula \( C = 2\pi r \):
\[
C = 2\pi \times 7 = 14\pi \text{ cm}
\]

#### Step 3: Calculate the Area
Using the formula \( A = \pi r^2 \):
\[
A = \pi \times 7^2 = \pi \times 49 = 49\pi \text{ cm}^2
\]

#### Final Answer:
\[
\boxed{14\pi \text{ cm}, 49\pi \text{ cm}^2}
\]

---

Problem 3:

- Given: Circumference \( C = 30\pi \) cm.
- Find: Radius and Area.

#### Step 1: Find the Radius
Using the formula \( C = 2\pi r \):
\[
30\pi = 2\pi r
\]
Divide both sides by \( 2\pi \):
\[
r = \frac{30\pi}{2\pi} = 15 \text{ cm}
\]

#### Step 2: Calculate the Area
Using the formula \( A = \pi r^2 \):
\[
A = \pi \times 15^2 = \pi \times 225 = 225\pi \text{ cm}^2
\]

#### Final Answer:
\[
\boxed{15 \text{ cm}, 225\pi \text{ cm}^2}
\]

---

Problem 4:

- Given: Area \( A = 100\pi \) cm².
- Find: Radius and Circumference.

#### Step 1: Find the Radius
Using the formula \( A = \pi r^2 \):
\[
100\pi = \pi r^2
\]
Divide both sides by \( \pi \):
\[
100 = r^2
\]
Take the square root of both sides:
\[
r = \sqrt{100} = 10 \text{ cm}
\]

#### Step 2: Calculate the Circumference
Using the formula \( C = 2\pi r \):
\[
C = 2\pi \times 10 = 20\pi \text{ cm}
\]

#### Final Answer:
\[
\boxed{10 \text{ cm}, 20\pi \text{ cm}}
\]

---

Final Summary of Answers:

1. \( 10\pi \text{ cm}, 25\pi \text{ cm}^2 \)
2. \( 14\pi \text{ cm}, 49\pi \text{ cm}^2 \)
3. \( 15 \text{ cm}, 225\pi \text{ cm}^2 \)
4. \( 10 \text{ cm}, 20\pi \text{ cm} \)

\[
\boxed{10\pi \text{ cm}, 25\pi \text{ cm}^2; 14\pi \text{ cm}, 49\pi \text{ cm}^2; 15 \text{ cm}, 225\pi \text{ cm}^2; 10 \text{ cm}, 20\pi \text{ cm}}
\]