Answer:
1387.2 ft² (nearest tenth)
Step-by-step explanation:
Formulae
- Circumference of a circle = [tex]2 \pi r[/tex]
- Area of a circle = [tex]\pi r^2[/tex]
(where r is the radius of the circle)
The railing of the circular fountain is the circumference of a circle.
The area of the fountain is the area of a circle.
First, find the radius by using the circumference formula:
Given:
[tex]\implies 132=2 \pi r[/tex]
[tex]\implies r=\dfrac{132}{2 \pi}=\dfrac{66}{\pi}[/tex]
Now input the found value of r into the formula for the area of a circle:
[tex]\begin{aligned}\implies \textsf{Area} & =\pi \left(\dfrac{66}{\pi}\right)^2\\\\ & = \dfrac{4356}{\pi}\\\\ & = \dfrac{4356}{3.14}\\\\ & = 1387.261146...\\\\ & = 1387.3 \: \sf ft^2\:(nearest\:tenth)\end{aligned}[/tex]
