Area of Circles | Mathematics worksheets, Circle math, 7th grade math - Free Printable

Problem Overview:

The task is to calculate the area of each circle given in the worksheet. The formula for the area of a circle is:

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

Where:
- \( \pi \) (pi) is approximately 3.14.
- \( r \) is the radius of the circle.

The diameter (\( d \)) of a circle is twice the radius (\( r \)), so:
\[
r = \frac{d}{2}
\]

We are asked to round the answers to the nearest hundredth.

Step-by-Step Solution:

#### 1. Circle H:
- Diameter (\( d \)) = 22 ft
- Radius (\( r \)) = \( \frac{d}{2} = \frac{22}{2} = 11 \) ft
- Area = \( \pi r^2 = 3.14 \times (11)^2 = 3.14 \times 121 = 379.94 \) sq ft

#### 2. Circle J:
- Radius (\( r \)) = 8 ft
- Area = \( \pi r^2 = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \) sq ft

#### 3. Circle F:
- Diameter (\( d \)) = 21 m
- Radius (\( r \)) = \( \frac{d}{2} = \frac{21}{2} = 10.5 \) m
- Area = \( \pi r^2 = 3.14 \times (10.5)^2 = 3.14 \times 110.25 = 346.19 \) sq m

#### 4. Circle t:
- Diameter (\( d \)) = 6 yd
- Radius (\( r \)) = \( \frac{d}{2} = \frac{6}{2} = 3 \) yd
- Area = \( \pi r^2 = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 \) sq yd

#### 5. Circle Q:
- Radius (\( r \)) = 31 m
- Area = \( \pi r^2 = 3.14 \times (31)^2 = 3.14 \times 961 = 3017.54 \) sq m

#### 6. Circle i:
- Diameter (\( d \)) = 14 yd
- Radius (\( r \)) = \( \frac{d}{2} = \frac{14}{2} = 7 \) yd
- Area = \( \pi r^2 = 3.14 \times (7)^2 = 3.14 \times 49 = 153.86 \) sq yd

#### 7. Circle b:
- Diameter (\( d \)) = 19 m
- Radius (\( r \)) = \( \frac{d}{2} = \frac{19}{2} = 9.5 \) m
- Area = \( \pi r^2 = 3.14 \times (9.5)^2 = 3.14 \times 90.25 = 283.39 \) sq m

#### 8. Circle a:
- Diameter (\( d \)) = 28 ft
- Radius (\( r \)) = \( \frac{d}{2} = \frac{28}{2} = 14 \) ft
- Area = \( \pi r^2 = 3.14 \times (14)^2 = 3.14 \times 196 = 615.44 \) sq ft

Final Answers:

1. Circle H: \( \boxed{379.94} \) sq ft
2. Circle J: \( \boxed{200.96} \) sq ft
3. Circle F: \( \boxed{346.19} \) sq m
4. Circle t: \( \boxed{28.26} \) sq yd
5. Circle Q: \( \boxed{3017.54} \) sq m
6. Circle i: \( \boxed{153.86} \) sq yd
7. Circle b: \( \boxed{283.39} \) sq m
8. Circle a: \( \boxed{615.44} \) sq ft

Explanation:

- For each circle, we identified whether the given measurement was the diameter or the radius.
- If the diameter was given, we calculated the radius by dividing the diameter by 2.
- We then used the formula \( \text{Area} = \pi r^2 \) to find the area.
- Finally, we rounded each result to the nearest hundredth as required.

This method ensures consistency and accuracy in solving all the problems.