Answer :
To determine the closest circumference and area of a circular table top with a diameter of 10 feet, follow these steps:
1. Determine the radius of the circle:
The radius \( r \) is half of the diameter. For a diameter of 10 feet:
[tex]\[ r = \frac{10}{2} = 5 \text{ feet} \][/tex]
2. Calculate the circumference:
The formula for the circumference \( C \) of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
Substituting the radius:
[tex]\[ C = 2 \pi \times 5 \approx 31.4 \text{ feet} \][/tex]
3. Calculate the area:
The formula for the area \( A \) of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the radius:
[tex]\[ A = \pi \times 5^2 = \pi \times 25 \approx 78.5 \text{ square feet} \][/tex]
Based on these calculations, the closest values for the circumference and area are:
- Circumference: approximately 31.4 feet
- Area: approximately 78.5 square feet
Therefore, the correct answer is:
B. 31.4 feet; 78.5 square feet
1. Determine the radius of the circle:
The radius \( r \) is half of the diameter. For a diameter of 10 feet:
[tex]\[ r = \frac{10}{2} = 5 \text{ feet} \][/tex]
2. Calculate the circumference:
The formula for the circumference \( C \) of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
Substituting the radius:
[tex]\[ C = 2 \pi \times 5 \approx 31.4 \text{ feet} \][/tex]
3. Calculate the area:
The formula for the area \( A \) of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the radius:
[tex]\[ A = \pi \times 5^2 = \pi \times 25 \approx 78.5 \text{ square feet} \][/tex]
Based on these calculations, the closest values for the circumference and area are:
- Circumference: approximately 31.4 feet
- Area: approximately 78.5 square feet
Therefore, the correct answer is:
B. 31.4 feet; 78.5 square feet
