QUESTION IMAGE
Question
find the circumference and area of the circle. round to the nearest tenth. 4. circle with radius 32 cm 5. circle with radius 15 yd 6. circle with diameter 5.8 km
Problem 4: Circle with radius \( r = 32 \, \text{cm} \)
Circumference:
The formula for the circumference of a circle is \( C = 2\pi r \).
Step 1: Substitute \( r = 32 \) into the formula
\( C = 2 \times \pi \times 32 \)
Step 2: Calculate the value
\( C = 64\pi \approx 64 \times 3.1416 \approx 201.1 \, \text{cm} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 32 \) into the formula
\( A = \pi \times (32)^2 \)
Step 2: Calculate the value
\( A = 1024\pi \approx 1024 \times 3.1416 \approx 3217.0 \, \text{cm}^2 \) (rounded to the nearest tenth)
Problem 5: Circle with radius \( r = 15 \, \text{yd} \)
Circumference:
The formula for the circumference of a circle is \( C = 2\pi r \).
Step 1: Substitute \( r = 15 \) into the formula
\( C = 2 \times \pi \times 15 \)
Step 2: Calculate the value
\( C = 30\pi \approx 30 \times 3.1416 \approx 94.2 \, \text{yd} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 15 \) into the formula
\( A = \pi \times (15)^2 \)
Step 2: Calculate the value
\( A = 225\pi \approx 225 \times 3.1416 \approx 706.9 \, \text{yd}^2 \) (rounded to the nearest tenth)
Problem 6: Circle with diameter \( d = 5.8 \, \text{km} \), so radius \( r = \frac{d}{2} = \frac{5.8}{2} = 2.9 \, \text{km} \)
Circumference:
The formula for the circumference of a circle is \( C = \pi d \) (or \( C = 2\pi r \)). Using \( C = \pi d \):
Step 1: Substitute \( d = 5.8 \) into the formula
\( C = \pi \times 5.8 \)
Step 2: Calculate the value
\( C \approx 5.8 \times 3.1416 \approx 18.2 \, \text{km} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 2.9 \) into the formula
\( A = \pi \times (2.9)^2 \)
Step 2: Calculate the value
\( A = \pi \times 8.41 \approx 8.41 \times 3.1416 \approx 26.4 \, \text{km}^2 \) (rounded to the nearest tenth)
Final Answers:
Problem 4:
- Circumference: \( \approx 201.1 \, \text{cm} \)
- Area: \( \approx 3217.0 \, \text{cm}^2 \)
Problem 5:
- Circumference: \( \approx 94.2 \, \text{yd} \)
- Area: \( \approx 706.9 \, \text{yd}^2 \)
Problem 6:
- Circumference: \( \approx 18.2 \, \text{km} \)
- Area: \( \approx 26.4 \, \text{km}^2 \)
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Problem 4: Circle with radius \( r = 32 \, \text{cm} \)
Circumference:
The formula for the circumference of a circle is \( C = 2\pi r \).
Step 1: Substitute \( r = 32 \) into the formula
\( C = 2 \times \pi \times 32 \)
Step 2: Calculate the value
\( C = 64\pi \approx 64 \times 3.1416 \approx 201.1 \, \text{cm} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 32 \) into the formula
\( A = \pi \times (32)^2 \)
Step 2: Calculate the value
\( A = 1024\pi \approx 1024 \times 3.1416 \approx 3217.0 \, \text{cm}^2 \) (rounded to the nearest tenth)
Problem 5: Circle with radius \( r = 15 \, \text{yd} \)
Circumference:
The formula for the circumference of a circle is \( C = 2\pi r \).
Step 1: Substitute \( r = 15 \) into the formula
\( C = 2 \times \pi \times 15 \)
Step 2: Calculate the value
\( C = 30\pi \approx 30 \times 3.1416 \approx 94.2 \, \text{yd} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 15 \) into the formula
\( A = \pi \times (15)^2 \)
Step 2: Calculate the value
\( A = 225\pi \approx 225 \times 3.1416 \approx 706.9 \, \text{yd}^2 \) (rounded to the nearest tenth)
Problem 6: Circle with diameter \( d = 5.8 \, \text{km} \), so radius \( r = \frac{d}{2} = \frac{5.8}{2} = 2.9 \, \text{km} \)
Circumference:
The formula for the circumference of a circle is \( C = \pi d \) (or \( C = 2\pi r \)). Using \( C = \pi d \):
Step 1: Substitute \( d = 5.8 \) into the formula
\( C = \pi \times 5.8 \)
Step 2: Calculate the value
\( C \approx 5.8 \times 3.1416 \approx 18.2 \, \text{km} \) (rounded to the nearest tenth)
Area:
The formula for the area of a circle is \( A = \pi r^2 \).
Step 1: Substitute \( r = 2.9 \) into the formula
\( A = \pi \times (2.9)^2 \)
Step 2: Calculate the value
\( A = \pi \times 8.41 \approx 8.41 \times 3.1416 \approx 26.4 \, \text{km}^2 \) (rounded to the nearest tenth)
Final Answers:
Problem 4:
- Circumference: \( \approx 201.1 \, \text{cm} \)
- Area: \( \approx 3217.0 \, \text{cm}^2 \)
Problem 5:
- Circumference: \( \approx 94.2 \, \text{yd} \)
- Area: \( \approx 706.9 \, \text{yd}^2 \)
Problem 6:
- Circumference: \( \approx 18.2 \, \text{km} \)
- Area: \( \approx 26.4 \, \text{km}^2 \)