Problem Overview:
The task is to calculate the area of several circles given their radii. The formula for the area of a circle is:
\[
\text{Area} = \pi r^2
\]
where \( r \) is the radius of the circle. We will use \( \pi \approx 3.14 \) and round the final answers to
1 decimal place.
Step-by-Step Solution:
####
Question 1: Calculate the area of the following circles.
1.
Circle (a): Radius = 4 cm
\[
\text{Area} = \pi r^2 = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \, \text{cm}^2
\]
Rounded to 1 decimal place:
50.2 cm²
2.
Circle (b): Radius = 7 cm
\[
\text{Area} = \pi r^2 = 3.14 \times (7)^2 = 3.14 \times 49 = 153.86 \, \text{cm}^2
\]
Rounded to 1 decimal place:
153.9 cm²
3.
Circle (c): Radius = 8 cm
\[
\text{Area} = \pi r^2 = 3.14 \times (8)^2 = 3.14 \times 64 = 200.96 \, \text{cm}^2
\]
Rounded to 1 decimal place:
201.0 cm²
4.
Circle (d): Radius = 10 m
\[
\text{Area} = \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \, \text{m}^2
\]
Rounded to 1 decimal place:
314.0 m²
5.
Circle (e): Radius = 1.5 m
\[
\text{Area} = \pi r^2 = 3.14 \times (1.5)^2 = 3.14 \times 2.25 = 7.065 \, \text{m}^2
\]
Rounded to 1 decimal place:
7.1 m²
6.
Circle (f): Radius = 50 cm
\[
\text{Area} = \pi r^2 = 3.14 \times (50)^2 = 3.14 \times 2500 = 7850 \, \text{cm}^2
\]
Rounded to 1 decimal place:
7850.0 cm²
7.
Circle (g): Radius = 7 mm
\[
\text{Area} = \pi r^2 = 3.14 \times (7)^2 = 3.14 \times 49 = 153.86 \, \text{mm}^2
\]
Rounded to 1 decimal place:
153.9 mm²
8.
Circle (h): Radius = 8.4 cm
\[
\text{Area} = \pi r^2 = 3.14 \times (8.4)^2 = 3.14 \times 70.56 = 221.5024 \, \text{cm}^2
\]
Rounded to 1 decimal place:
221.5 cm²
Final Answers for Question 1:
\[
\boxed{
\begin{aligned}
&\text{(a)} \, 50.2 \, \text{cm}^2, \, \text{(b)} \, 153.9 \, \text{cm}^2, \, \text{(c)} \, 201.0 \, \text{cm}^2, \, \text{(d)} \, 314.0 \, \text{m}^2, \\
&\text{(e)} \, 7.1 \, \text{m}^2, \, \text{(f)} \, 7850.0 \, \text{cm}^2, \, \text{(g)} \, 153.9 \, \text{mm}^2, \, \text{(h)} \, 221.5 \, \text{cm}^2
\end{aligned}
}
\]
####
Question 2: Calculate the area of the following circles.
Since the image does not provide the details for Question 2, I cannot solve it. Please provide the radii or diameters for the circles in Question 2 if you need further assistance.
Summary:
- Used the formula \( \text{Area} = \pi r^2 \).
- Rounded all answers to 1 decimal place.
- Provided detailed calculations for each circle in Question 1.
If you have any more questions or need further clarification, feel free to ask!
Parent Tip: Review the logic above to help your child master the concept of area of a circle worksheet.
