Area of Circles worksheet with problems and examples for calculating circle area using radius and diameter.

To solve the problem of finding the area of each circle, we will use the formula for the area of a circle:

\[
\text{Area} = \pi r^2
\]

where \( r \) is the radius of the circle. If the diameter \( d \) is given instead of the radius, we can find the radius using the relationship:

\[
r = \frac{d}{2}
\]

Let's solve each part step by step.

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1. Circle with Radius \( 6 \, \text{in} \)

- Given: Radius \( r = 6 \, \text{in} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (6)^2 = \pi \cdot 36 \)
- Result: \( \text{Area} = 36\pi \, \text{in}^2 \)

Answer: \( 36\pi \, \text{in}^2 \)

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2. Circle with Diameter \( 28 \, \text{ft} \)

- Given: Diameter \( d = 28 \, \text{ft} \)
- Find Radius: \( r = \frac{d}{2} = \frac{28}{2} = 14 \, \text{ft} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (14)^2 = \pi \cdot 196 \)
- Result: \( \text{Area} = 196\pi \, \text{ft}^2 \)

Answer: \( 196\pi \, \text{ft}^2 \)

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3. Circle with Diameter \( 0.22 \, \text{m} \)

- Given: Diameter \( d = 0.22 \, \text{m} \)
- Find Radius: \( r = \frac{d}{2} = \frac{0.22}{2} = 0.11 \, \text{m} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (0.11)^2 = \pi \cdot 0.0121 \)
- Result: \( \text{Area} = 0.0121\pi \, \text{m}^2 \)

Answer: \( 0.0121\pi \, \text{m}^2 \)

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4. Circle with Diameter \( 22 \, \text{ft} \)

- Given: Diameter \( d = 22 \, \text{ft} \)
- Find Radius: \( r = \frac{d}{2} = \frac{22}{2} = 11 \, \text{ft} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (11)^2 = \pi \cdot 121 \)
- Result: \( \text{Area} = 121\pi \, \text{ft}^2 \)

Answer: \( 121\pi \, \text{ft}^2 \)

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5. Circle with Radius \( 3.9 \, \text{in} \)

- Given: Radius \( r = 3.9 \, \text{in} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (3.9)^2 = \pi \cdot 15.21 \)
- Result: \( \text{Area} = 15.21\pi \, \text{in}^2 \)

Answer: \( 15.21\pi \, \text{in}^2 \)

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6. Circle with Diameter \( 23 \, \text{yd} \)

- Given: Diameter \( d = 23 \, \text{yd} \)
- Find Radius: \( r = \frac{d}{2} = \frac{23}{2} = 11.5 \, \text{yd} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (11.5)^2 = \pi \cdot 132.25 \)
- Result: \( \text{Area} = 132.25\pi \, \text{yd}^2 \)

Answer: \( 132.25\pi \, \text{yd}^2 \)

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7. Circle with Radius \( 5 \, \text{yd} \)

- Given: Radius \( r = 5 \, \text{yd} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (5)^2 = \pi \cdot 25 \)
- Result: \( \text{Area} = 25\pi \, \text{yd}^2 \)

Answer: \( 25\pi \, \text{yd}^2 \)

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8. Circle with Diameter \( 1.2 \, \text{ft} \)

- Given: Diameter \( d = 1.2 \, \text{ft} \)
- Find Radius: \( r = \frac{d}{2} = \frac{1.2}{2} = 0.6 \, \text{ft} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (0.6)^2 = \pi \cdot 0.36 \)
- Result: \( \text{Area} = 0.36\pi \, \text{ft}^2 \)

Answer: \( 0.36\pi \, \text{ft}^2 \)

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9. Circle with Diameter \( 4 \, \text{in} \)

- Given: Diameter \( d = 4 \, \text{in} \)
- Find Radius: \( r = \frac{d}{2} = \frac{4}{2} = 2 \, \text{in} \)
- Formula: \( \text{Area} = \pi r^2 \)
- Substitute: \( \text{Area} = \pi (2)^2 = \pi \cdot 4 \)
- Result: \( \text{Area} = 4\pi \, \text{in}^2 \)

Answer: \( 4\pi \, \text{in}^2 \)

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Final Answers

\[
\boxed{
\begin{array}{ll}
\text{1. } 36\pi \, \text{in}^2 & \text{2. } 196\pi \, \text{ft}^2 \\
\text{3. } 0.0121\pi \, \text{m}^2 & \text{4. } 121\pi \, \text{ft}^2 \\
\text{5. } 15.21\pi \, \text{in}^2 & \text{6. } 132.25\pi \, \text{yd}^2 \\
\text{7. } 25\pi \, \text{yd}^2 & \text{8. } 0.36\pi \, \text{ft}^2 \\
\text{9. } 4\pi \, \text{in}^2 &
\end{array}
}
\]