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Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?

A. [tex]\(7 \pi \, m^2\)[/tex]
B. [tex]\(14 \pi \, m^2\)[/tex]
C. [tex]\(28 \pi \, m^2\)[/tex]
D. [tex]\(49 \pi \, m^2\)[/tex]

Sagot :

GinnyAnswer
To determine the area of Fiona's circle, we need to follow these steps:

1. Calculate the radius of the circle:
- The diameter of the circle is given as 14 meters.
- The radius ([tex]\( r \)[/tex]) is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ meters} \][/tex]

2. Calculate the area of the circle:
- The formula for the area ([tex]\( A \)[/tex]) of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
- Substituting the radius we found:
[tex]\[ r^2 = 7^2 = 49 \][/tex]
- Therefore:
[tex]\[ A = \pi \times 49 = 49 \pi \text{ square meters} \][/tex]

Using these steps, we find that the area of Fiona's circle is [tex]\( 49 \pi \)[/tex] square meters.

So, the correct option is:
[tex]\[ \boxed{49 \pi m^2} \][/tex]
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