The best approximation for the area of a circle with a diameter of 13 meters from the listed options is: Option D: 530. 7 m²
Suppose the circle has radius of 'r' units, then, its area is given as:
[tex]A = \pi \times (r)^2[/tex] sq. units
Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:
[tex]A = \pi \times (\dfrac{d}{2})^2[/tex] sq. units
For the given case, the circle has got its diameter of 13 meters, so its area is evaluated as:
[tex]A = \pi \times (\dfrac{d}{2})^2 \approx 3.14 \times 13^2 = 530.66 \approx 530.7\: \rm m^2[/tex]
(used pi = 3.14 as said in the problem).
Thus, the best approximation for the area of a circle with a diameter of 13 meters from the listed options is: Option D: 530. 7 m²
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