Question
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
50 feet
50 feet
6 feet
6 feet
13 feet
13 feet
25 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
𝜋
.(1 point)
Responses
10.21 meters
10.21 meters
10.22 meters
10.22 meters
33.18 meters
33.18 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
𝜋
.(1 point)
Responses
16 feet
16 feet
15.7 feet
15.7 feet
15.6 feet
15.6 feet
7.85 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
𝜋
.(1 point)
Responses
452.2 square feet
452.2 square feet
75.4 square feet
75.4 square feet
452.16 square feet
452.16 square feet
113.04 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
𝜋
.(1 point)
Responses
15.7 square mm
15.7 square mm
78.5 square mm
78.5 square mm
79 square mm
79 square mm
314 square mm
Responses
50 feet
50 feet
6 feet
6 feet
13 feet
13 feet
25 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
𝜋
.(1 point)
Responses
10.21 meters
10.21 meters
10.22 meters
10.22 meters
33.18 meters
33.18 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
𝜋
.(1 point)
Responses
16 feet
16 feet
15.7 feet
15.7 feet
15.6 feet
15.6 feet
7.85 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
𝜋
.(1 point)
Responses
452.2 square feet
452.2 square feet
75.4 square feet
75.4 square feet
452.16 square feet
452.16 square feet
113.04 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
𝜋
.(1 point)
Responses
15.7 square mm
15.7 square mm
78.5 square mm
78.5 square mm
79 square mm
79 square mm
314 square mm
Answers
GPT-4o mini
Let's calculate each of the requested values step-by-step:
1. **Circumference of a circle with a diameter of 4 feet:**
\[
C = \pi \times d
\]
Using \(\pi \approx 3.14\):
\[
C = 3.14 \times 4 = 12.56 \text{ feet}
\]
The best estimate for the circumference is **13 feet**.
2. **Circumference of a circle with a diameter of 3.25 meters:**
\[
C = \pi \times d
\]
Using \(\pi \approx 3.14\):
\[
C = 3.14 \times 3.25 = 10.205 \text{ meters}
\]
Rounding to the hundredths place, the answer is **10.21 meters**.
3. **Circumference of a circle with a radius of 2.5 feet:**
\[
C = 2 \times \pi \times r
\]
Using \(\pi \approx 3.14\):
\[
C = 2 \times 3.14 \times 2.5 = 15.7 \text{ feet}
\]
The estimate rounded to the tenths place is **15.7 feet**.
4. **Area of a circle with a radius of 12 feet:**
\[
A = \pi \times r^2
\]
Using \(\pi \approx 3.14\):
\[
A = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 \text{ square feet}
\]
The estimate rounded to the hundredths place is **452.16 square feet**.
5. **Area of a circle with a diameter of 10 millimeters:**
First, find the radius:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \text{ mm}
\]
Now compute the area:
\[
A = \pi \times r^2
\]
Using \(\pi \approx 3.14\):
\[
A = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 \text{ square mm}
\]
The estimate rounded to the tenths place is **78.5 square mm**.
To summarize:
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 of 4 feet:**
\[
C = \pi \times d
\]
Using \(\pi \approx 3.14\):
\[
C = 3.14 \times 4 = 12.56 \text{ feet}
\]
The best estimate for the circumference is **13 feet**.
2. **Circumference of a circle with a diameter of 3.25 meters:**
\[
C = \pi \times d
\]
Using \(\pi \approx 3.14\):
\[
C = 3.14 \times 3.25 = 10.205 \text{ meters}
\]
Rounding to the hundredths place, the answer is **10.21 meters**.
3. **Circumference of a circle with a radius of 2.5 feet:**
\[
C = 2 \times \pi \times r
\]
Using \(\pi \approx 3.14\):
\[
C = 2 \times 3.14 \times 2.5 = 15.7 \text{ feet}
\]
The estimate rounded to the tenths place is **15.7 feet**.
4. **Area of a circle with a radius of 12 feet:**
\[
A = \pi \times r^2
\]
Using \(\pi \approx 3.14\):
\[
A = 3.14 \times (12)^2 = 3.14 \times 144 = 452.16 \text{ square feet}
\]
The estimate rounded to the hundredths place is **452.16 square feet**.
5. **Area of a circle with a diameter of 10 millimeters:**
First, find the radius:
\[
r = \frac{d}{2} = \frac{10}{2} = 5 \text{ mm}
\]
Now compute the area:
\[
A = \pi \times r^2
\]
Using \(\pi \approx 3.14\):
\[
A = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 \text{ square mm}
\]
The estimate rounded to the tenths place is **78.5 square mm**.
To summarize:
1. 13 feet
2. 10.21 meters
3. 15.7 feet
4. 452.16 square feet
5. 78.5 square mm