Answer :
To determine how much material is needed to make a circular tablecloth with a diameter of 4 feet, we need to calculate the area of the circle. The steps to find the area of a circle are as follows:
1. Determine the Radius:
The diameter of the circle is given as 4 feet. The radius (r) is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ feet} \][/tex]
2. Calculate the Area:
The formula to find the area (A) of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Here, [tex]\(\pi\)[/tex] (pi) is approximately 3.14159.
Using the radius we found:
[tex]\[ A = \pi \times (2 \text{ feet})^2 \][/tex]
[tex]\[ A = \pi \times 4 \text{ square feet} \][/tex]
[tex]\[ A \approx 3.14159 \times 4 \][/tex]
[tex]\[ A \approx 12.56636 \text{ square feet} \][/tex]
3. Round to the Nearest Hundredth:
We now need to round the area to the nearest hundredth of a square foot.
[tex]\[ A \approx 12.57 \text{ square feet} \][/tex]
Thus, the amount of material needed to make the circular tablecloth with a diameter of 4 feet is approximately 12.57 square feet, rounded to the nearest hundredth.
1. Determine the Radius:
The diameter of the circle is given as 4 feet. The radius (r) is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ feet} \][/tex]
2. Calculate the Area:
The formula to find the area (A) of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Here, [tex]\(\pi\)[/tex] (pi) is approximately 3.14159.
Using the radius we found:
[tex]\[ A = \pi \times (2 \text{ feet})^2 \][/tex]
[tex]\[ A = \pi \times 4 \text{ square feet} \][/tex]
[tex]\[ A \approx 3.14159 \times 4 \][/tex]
[tex]\[ A \approx 12.56636 \text{ square feet} \][/tex]
3. Round to the Nearest Hundredth:
We now need to round the area to the nearest hundredth of a square foot.
[tex]\[ A \approx 12.57 \text{ square feet} \][/tex]
Thus, the amount of material needed to make the circular tablecloth with a diameter of 4 feet is approximately 12.57 square feet, rounded to the nearest hundredth.
