Question

finding an area find the area of the circle. use 3.14 or \\(\frac{22}{7}\\).

1. image of a recycling symbol with 9 mm measurement
2. image of a wi - fi symbol with 14 cm measurement
3. image of a tree - ring with 10 in. measurement
4. image of a can top with 3 in. measurement
5. image of a peppermint with 2 cm measurement
6. image of a dartboard with 1.5 ft measurement

Explanation:

To find the area of a circle, we use the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle (half of the diameter). Let's solve each problem one by one (assuming the given measurements are diameters; if they are radii, we skip the first step of dividing by 2):

Problem 7: Diameter = 9 mm

Step 1: Find the radius

The radius \( r \) is half the diameter.
\( r = \frac{9}{2} = 4.5 \) mm

Step 2: Calculate the area

Using \( A = \pi r^2 \) and \( \pi \approx \frac{22}{7} \) or \( 3.14 \). Let’s use \( \frac{22}{7} \):
\( A = \frac{22}{7} \times (4.5)^2 \)
First, \( 4.5^2 = 20.25 \)
\( A = \frac{22}{7} \times 20.25 \approx \frac{22 \times 20.25}{7} \approx \frac{445.5}{7} \approx 63.64 \) mm² (or with \( \pi = 3.14 \): \( 3.14 \times 20.25 = 63.585 \) mm²)

Problem 8: Diameter = 14 cm

Step 1: Find the radius

\( r = \frac{14}{2} = 7 \) cm

Step 2: Calculate the area

Using \( A = \pi r^2 \) and \( \pi = \frac{22}{7} \):
\( A = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154 \) cm²

Problem 9: Diameter = 10 in (assuming the top - left circle has diameter 10 in)

Step 1: Find the radius

\( r = \frac{10}{2} = 5 \) in

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \) in² (or with \( \frac{22}{7} \): \( \frac{22}{7} \times 25 \approx 78.57 \) in²)

Problem 10: Diameter = 3 in (assuming the bottom - left circle has diameter 3 in)

Step 1: Find the radius

\( r = \frac{3}{2} = 1.5 \) in

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times (1.5)^2 = 3.14 \times 2.25 = 7.065 \) in²

Problem 11: Diameter = 2 cm (assuming the peppermint - shaped circle has diameter 2 cm)

Step 1: Find the radius

\( r = \frac{2}{2} = 1 \) cm

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times 1^2 = 3.14 \) cm²

Problem 12: Diameter = 1.5 ft (assuming the target - shaped circle has diameter 1.5 ft)

Step 1: Find the radius

\( r = \frac{1.5}{2} = 0.75 \) ft

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times (0.75)^2 = 3.14 \times 0.5625 = 1.76625 \) ft²

Summary of Answers (using \( \pi = 3.14 \) or \( \frac{22}{7} \) as appropriate):

• 7. \( \boldsymbol{\approx 63.59} \) mm² (or \( 63.64 \) mm² with \( \frac{22}{7} \))
• 8. \( \boldsymbol{154} \) cm²
• 9. \( \boldsymbol{\approx 78.5} \) in²
• 10. \( \boldsymbol{\approx 7.07} \) in²
• 11. \( \boldsymbol{3.14} \) cm²
• 12. \( \boldsymbol{\approx 1.77} \) ft²

(Note: If the given measurements are radii instead of diameters, skip the “find radius” step and use the given value directly in \( A = \pi r^2 \).)

Answer:

To find the area of a circle, we use the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle (half of the diameter). Let's solve each problem one by one (assuming the given measurements are diameters; if they are radii, we skip the first step of dividing by 2):

Problem 7: Diameter = 9 mm

Step 1: Find the radius

The radius \( r \) is half the diameter.
\( r = \frac{9}{2} = 4.5 \) mm

Step 2: Calculate the area

Using \( A = \pi r^2 \) and \( \pi \approx \frac{22}{7} \) or \( 3.14 \). Let’s use \( \frac{22}{7} \):
\( A = \frac{22}{7} \times (4.5)^2 \)
First, \( 4.5^2 = 20.25 \)
\( A = \frac{22}{7} \times 20.25 \approx \frac{22 \times 20.25}{7} \approx \frac{445.5}{7} \approx 63.64 \) mm² (or with \( \pi = 3.14 \): \( 3.14 \times 20.25 = 63.585 \) mm²)

Problem 8: Diameter = 14 cm

Step 1: Find the radius

\( r = \frac{14}{2} = 7 \) cm

Step 2: Calculate the area

Using \( A = \pi r^2 \) and \( \pi = \frac{22}{7} \):
\( A = \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154 \) cm²

Problem 9: Diameter = 10 in (assuming the top - left circle has diameter 10 in)

Step 1: Find the radius

\( r = \frac{10}{2} = 5 \) in

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \) in² (or with \( \frac{22}{7} \): \( \frac{22}{7} \times 25 \approx 78.57 \) in²)

Problem 10: Diameter = 3 in (assuming the bottom - left circle has diameter 3 in)

Step 1: Find the radius

\( r = \frac{3}{2} = 1.5 \) in

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times (1.5)^2 = 3.14 \times 2.25 = 7.065 \) in²

Problem 11: Diameter = 2 cm (assuming the peppermint - shaped circle has diameter 2 cm)

Step 1: Find the radius

\( r = \frac{2}{2} = 1 \) cm

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times 1^2 = 3.14 \) cm²

Problem 12: Diameter = 1.5 ft (assuming the target - shaped circle has diameter 1.5 ft)

Step 1: Find the radius

\( r = \frac{1.5}{2} = 0.75 \) ft

Step 2: Calculate the area

Using \( \pi = 3.14 \):
\( A = 3.14 \times (0.75)^2 = 3.14 \times 0.5625 = 1.76625 \) ft²

Summary of Answers (using \( \pi = 3.14 \) or \( \frac{22}{7} \) as appropriate):

• 7. \( \boldsymbol{\approx 63.59} \) mm² (or \( 63.64 \) mm² with \( \frac{22}{7} \))
• 8. \( \boldsymbol{154} \) cm²
• 9. \( \boldsymbol{\approx 78.5} \) in²
• 10. \( \boldsymbol{\approx 7.07} \) in²
• 11. \( \boldsymbol{3.14} \) cm²
• 12. \( \boldsymbol{\approx 1.77} \) ft²

(Note: If the given measurements are radii instead of diameters, skip the “find radius” step and use the given value directly in \( A = \pi r^2 \).)