To find the difference between the areas of two circular tables with given diameters, we will follow these steps:
1. Determine the radius of each table:
- The diameter of the first table is 8 feet. The radius is half of the diameter.
[tex]\[
\text{Radius}_1 = \frac{8}{2} = 4 \text{ feet}
\][/tex]
- The diameter of the second table is 10 feet. The radius is half of the diameter.
[tex]\[
\text{Radius}_2 = \frac{10}{2} = 5 \text{ feet}
\][/tex]
2. Calculate the area of each table using the formula for the area of a circle [tex]\((A = \pi r^2)\)[/tex]:
- For the first table:
[tex]\[
A_1 = \pi \times (4)^2 = \pi \times 16 \approx 3.14159 \times 16 \approx 50.26548 \text{ square feet}
\][/tex]
- For the second table:
[tex]\[
A_2 = \pi \times (5)^2 = \pi \times 25 \approx 3.14159 \times 25 \approx 78.53982 \text{ square feet}
\][/tex]
3. Find the difference between the two areas:
[tex]\[
\text{Area Difference} = A_2 - A_1 \approx 78.53982 - 50.26548 \approx 28.27434 \text{ square feet}
\][/tex]
4. Round the difference to the nearest hundredth:
[tex]\[
\text{Area Difference (rounded)} \approx 28.27 \text{ square feet}
\][/tex]
Therefore, the difference between the two areas, rounded to the nearest hundredth, is approximately [tex]\(28.27\)[/tex] square feet.
