Answer:
[tex]6361.7[/tex] square feet
Step-by-step explanation:
To find the area ([tex]A[/tex]) of a circle, we can use the formula:
[tex] A = \pi r^2 [/tex]
where [tex]r[/tex] is the radius of the circle. The radius ([tex]r[/tex]) is half of the diameter ([tex]d[/tex]), so [tex]r = \dfrac{d}{2}[/tex].
Given that the diameter of the sundial's circular base is 90 feet, the radius is [tex]r = \dfrac{90}{2} = 45[/tex] feet.
Now, substitute this value into the area formula:
[tex] A = \pi \times (45)^2 [/tex]
[tex] A \approx \pi \times 2025 [/tex]
Since we're looking for an approximation, we can use [tex]\pi[/tex] as approximately 3.14:
[tex] A \approx 3.141592654 \times 2025 [/tex]
[tex] A \approx 6361.725124 [/tex]
[tex] A \approx 6361.7 \textsf{(in nearest tenth)}[/tex]
So, the area of the circular base of the sundial is closest to [tex]6361.7[/tex] square feet.
