Problem Description:
The task is to calculate the area of each circle given in the worksheet. The diameters of the circles are provided, and we need to use the formula for the area of a circle:
\[
\text{Area} = \pi r^2
\]
where \( r \) is the radius of the circle. Since the diameter \( d \) is given, we can find the radius using the relationship:
\[
r = \frac{d}{2}
\]
We will use \( \pi \approx 3.14 \) for calculations.
---
Step-by-Step Solution:
####
Circle 1:
- Diameter (\( d \)) = 8 yd
- Radius (\( r \)) = \( \frac{8}{2} = 4 \) yd
- Area = \( \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \) square yards
####
Circle 2:
- Diameter (\( d \)) = 18 in
- Radius (\( r \)) = \( \frac{18}{2} = 9 \) in
- Area = \( \pi r^2 = 3.14 \times 9^2 = 3.14 \times 81 = 254.34 \) square inches
####
Circle 3:
- Diameter (\( d \)) = 10 yd
- Radius (\( r \)) = \( \frac{10}{2} = 5 \) yd
- Area = \( \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \) square yards
####
Circle 4:
- Diameter (\( d \)) = 6 in
- Radius (\( r \)) = \( \frac{6}{2} = 3 \) in
- Area = \( \pi r^2 = 3.14 \times 3^2 = 3.14 \times 9 = 28.26 \) square inches
####
Circle 5:
- Diameter (\( d \)) = 4 ft
- Radius (\( r \)) = \( \frac{4}{2} = 2 \) ft
- Area = \( \pi r^2 = 3.14 \times 2^2 = 3.14 \times 4 = 12.56 \) square feet
####
Circle 6:
- Diameter (\( d \)) = 10 ft
- Radius (\( r \)) = \( \frac{10}{2} = 5 \) ft
- Area = \( \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \) square feet
####
Circle 7:
- Diameter (\( d \)) = 1 yd
- Radius (\( r \)) = \( \frac{1}{2} = 0.5 \) yd
- Area = \( \pi r^2 = 3.14 \times (0.5)^2 = 3.14 \times 0.25 = 0.785 \) square yards
####
Circle 8:
- Diameter (\( d \)) = 14 in
- Radius (\( r \)) = \( \frac{14}{2} = 7 \) in
- Area = \( \pi r^2 = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \) square inches
####
Circle 9:
- Diameter (\( d \)) = 2 yd
- Radius (\( r \)) = \( \frac{2}{2} = 1 \) yd
- Area = \( \pi r^2 = 3.14 \times 1^2 = 3.14 \times 1 = 3.14 \) square yards
---
Final Answers:
1. \( 50.24 \) square yards
2. \( 254.34 \) square inches
3. \( 78.5 \) square yards
4. \( 28.26 \) square inches
5. \( 12.56 \) square feet
6. \( 78.5 \) square feet
7. \( 0.785 \) square yards
8. \( 153.86 \) square inches
9. \( 3.14 \) square yards
\[
\boxed{50.24, 254.34, 78.5, 28.26, 12.56, 78.5, 0.785, 153.86, 3.14}
\]
Parent Tip: Review the logic above to help your child master the concept of parts of a circle worksheet.