Let's go through each question one by one:
1. **Circumference of a circle with a diameter = 4 feet:**
The formula for the circumference of a circle is:
\[
C = \pi \times \text{diameter}
\]
Using \(\pi \approx 3.14\):
\[
C = 3.14 \times 4 = 12.56 \text{ feet}
\]
The closest estimate among the given choices is:
\[
\text{13 feet}
\]
2. **Circumference of a circle with a diameter of 3.25 meters:**
Using the formula:
\[
C = \pi \times \text{diameter}
\]
With \(\pi \approx 3.14\):
\[
C = 3.14 \times 3.25 = 10.205 \text{ meters}
\]
Rounded to the hundredths place, it is:
\[
10.21 \text{ meters}
\]
3. **Circumference of a circle with a radius of 2.5 feet:**
First, find the diameter:
\[
\text{Diameter} = 2 \times \text{radius} = 2 \times 2.5 = 5 \text{ feet}
\]
Using the circumference formula with \(\pi \approx 3.14\):
\[
C = 3.14 \times 5 = 15.7 \text{ feet}
\]
4. **Area of a circle with a radius of 12 feet:**
The formula for the area of a circle is:
\[
A = \pi \times (\text{radius})^2
\]
Using \(\pi \approx 3.14\):
\[
A = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 \text{ square feet}
\]
5. **Area of a circle with a diameter of 10 millimeters:**
First, find the radius:
\[
\text{Radius} = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ mm}
\]
Using the area formula with \(\pi \approx 3.14\):
\[
A = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 \text{ square mm}
\]
So, the answers are:
1. 13 feet
2. 10.21 meters
3. 15.7 feet
4. 452.16 square feet
5. 78.5 square mm
Estimate Values of Expressions with Pi Quick Check
What is the circumference of a circle with a diameter = 4 feet? Which of the following is the best estimation for the circumference?(1 point)
Responses
6 feet
6 feet
50 feet
50 feet
25 feet
25 feet
13 feet
2. What is the circumference of a circle with a diameter of 3.25 meters? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
10.22 meters
10.22 meters
33.18 meters
33.18 meters
10.21 meters
10.21 meters
10.2 meters
3. What is the circumference of a circle with a radius of 2.5 feet? Estimate the circumference to the tenths place using 3.14 for π
.(1 point)
Responses
15.6 feet
15.6 feet
15.7 feet
15.7 feet
7.85 feet
7.85 feet
16 feet
4. What is the area of a circle with a radius of 12 feet? Estimate the area to the hundredths place using 3.14 for π
.(1 point)
Responses
75.4 square feet
75.4 square feet
452.2 square feet
452.2 square feet
113.04 square feet
113.04 square feet
452.16 square feet
5. What is the area of a circle with a diameter of 10 millimeters? Estimate the area to the tenths place using 3.14 for π
.(1 point)
Responses
78.5 square mm
78.5 square mm
15.7 square mm
15.7 square mm
79 square mm
79 square mm
314 square mm
3 answers
sure?
Yes, let's review the calculations to confirm the answers:
1. **Circumference of a circle with a diameter = 4 feet:**
\[
C = \pi \times \text{diameter} \approx 3.14 \times 4 = 12.56 \text{ feet}
\]
The closest choice is:
\[
13 \text{ feet}
\]
2. **Circumference of a circle with a diameter of 3.25 meters:**
\[
C = \pi \times \text{diameter} \approx 3.14 \times 3.25 = 10.205 \text{ meters}
\]
Rounded to the hundredths place:
\[
10.21 \text{ meters}
\]
3. **Circumference of a circle with a radius of 2.5 feet:**
\[
\text{Diameter} = 2 \times \text{radius} = 2 \times 2.5 = 5 \text{ feet}
\]
\[
C = \pi \times \text{diameter} \approx 3.14 \times 5 = 15.7 \text{ feet}
\]
4. **Area of a circle with a radius of 12 feet:**
\[
A = \pi \times (\text{radius})^2 \approx 3.14 \times 12^2 = 3.14 \times 144 = 452.16 \text{ square feet}
\]
5. **Area of a circle with a diameter of 10 millimeters:**
\[
\text{Radius} = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ mm}
\]
\[
A = \pi \times (\text{radius})^2 \approx 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ square mm}
\]
All calculations have been verified, so the answers are indeed:
1. 13 feet
2. 10.21 meters
3. 15.7 feet
4. 452.16 square feet
5. 78.5 square mm
1. **Circumference of a circle with a diameter = 4 feet:**
\[
C = \pi \times \text{diameter} \approx 3.14 \times 4 = 12.56 \text{ feet}
\]
The closest choice is:
\[
13 \text{ feet}
\]
2. **Circumference of a circle with a diameter of 3.25 meters:**
\[
C = \pi \times \text{diameter} \approx 3.14 \times 3.25 = 10.205 \text{ meters}
\]
Rounded to the hundredths place:
\[
10.21 \text{ meters}
\]
3. **Circumference of a circle with a radius of 2.5 feet:**
\[
\text{Diameter} = 2 \times \text{radius} = 2 \times 2.5 = 5 \text{ feet}
\]
\[
C = \pi \times \text{diameter} \approx 3.14 \times 5 = 15.7 \text{ feet}
\]
4. **Area of a circle with a radius of 12 feet:**
\[
A = \pi \times (\text{radius})^2 \approx 3.14 \times 12^2 = 3.14 \times 144 = 452.16 \text{ square feet}
\]
5. **Area of a circle with a diameter of 10 millimeters:**
\[
\text{Radius} = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ mm}
\]
\[
A = \pi \times (\text{radius})^2 \approx 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ square mm}
\]
All calculations have been verified, so the answers are indeed:
1. 13 feet
2. 10.21 meters
3. 15.7 feet
4. 452.16 square feet
5. 78.5 square mm