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The diameter of a circle is 14 feet. What is the area of the circle in terms of [tex]$\pi$[/tex]?

A. [tex]28 \pi \, \text{ft}^2[/tex]
B. [tex]196 \pi \, \text{ft}^2[/tex]
C. [tex]14 \pi \, \text{ft}^2[/tex]
D. [tex]49 \pi \, \text{ft}^2[/tex]


Sagot :

Let's go through the solution step-by-step to determine the area of the circle in terms of [tex]\(\pi\)[/tex]:

1. Understand the given information:
- Diameter of the circle, [tex]\( d = 14 \)[/tex] feet.

2. Calculate the radius:
- The radius [tex]\( r \)[/tex] of a circle is half of its diameter.
[tex]\[ r = \frac{d}{2} = \frac{14 \, \text{feet}}{2} = 7 \, \text{feet} \][/tex]

3. Recall the formula for the area of a circle:
- The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]

4. Substitute the radius into the area formula:
- Substitute [tex]\( r = 7 \, \text{feet} \)[/tex] into the formula:
[tex]\[ A = \pi (7 \, \text{feet})^2 = \pi (49 \, \text{feet}^2) = 49\pi \, \text{feet}^2 \][/tex]

5. Match the calculated area with the given options:
- The correct area in terms of [tex]\(\pi\)[/tex] is:
[tex]\[ 49\pi \, \text{feet}^2 \][/tex]

Therefore, the answer is:

[tex]\[ \boxed{49\pi \, \text{ft}^2} \][/tex]
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