Answer :
To find the radius of a circle given its area, we need to use the formula for the area of a circle, which is:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius.
Given:
[tex]\[ A = 379.94 \text{ square inches} \][/tex]
[tex]\[ \pi \approx 3.14 \][/tex]
We need to solve for [tex]\( r \)[/tex]. Plugging in the given values, the equation becomes:
[tex]\[ 379.94 = 3.14 \cdot r^2 \][/tex]
To isolate [tex]\( r^2 \)[/tex], we need to divide both sides of the equation by 3.14:
[tex]\[ r^2 = \frac{379.94}{3.14} \][/tex]
To find [tex]\( r \)[/tex], we take the square root of both sides:
[tex]\[ r = \sqrt{\frac{379.94}{3.14}} \][/tex]
Now, let’s review the provided choices:
A. [tex]\( 379.94 = 3.14 \cdot r \cdot r \)[/tex]
B. [tex]\( 379.94 \cdot 2 = r \cdot 3.14 \)[/tex]
C. [tex]\( 379.94 \cdot 3.14 + 2 \cdot r \)[/tex]
Option A correctly represents the original equation for the area of a circle, where [tex]\( \pi \approx 3.14 \)[/tex] and the radius squared ([tex]\( r \cdot r \)[/tex]) is multiplied by π.
Therefore, the correct equation to use is:
[tex]\[ \boxed{\text{A. } 379.94 = 3.14 \cdot r \cdot r} \][/tex]
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( A \)[/tex] is the area, [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14, and [tex]\( r \)[/tex] is the radius.
Given:
[tex]\[ A = 379.94 \text{ square inches} \][/tex]
[tex]\[ \pi \approx 3.14 \][/tex]
We need to solve for [tex]\( r \)[/tex]. Plugging in the given values, the equation becomes:
[tex]\[ 379.94 = 3.14 \cdot r^2 \][/tex]
To isolate [tex]\( r^2 \)[/tex], we need to divide both sides of the equation by 3.14:
[tex]\[ r^2 = \frac{379.94}{3.14} \][/tex]
To find [tex]\( r \)[/tex], we take the square root of both sides:
[tex]\[ r = \sqrt{\frac{379.94}{3.14}} \][/tex]
Now, let’s review the provided choices:
A. [tex]\( 379.94 = 3.14 \cdot r \cdot r \)[/tex]
B. [tex]\( 379.94 \cdot 2 = r \cdot 3.14 \)[/tex]
C. [tex]\( 379.94 \cdot 3.14 + 2 \cdot r \)[/tex]
Option A correctly represents the original equation for the area of a circle, where [tex]\( \pi \approx 3.14 \)[/tex] and the radius squared ([tex]\( r \cdot r \)[/tex]) is multiplied by π.
Therefore, the correct equation to use is:
[tex]\[ \boxed{\text{A. } 379.94 = 3.14 \cdot r \cdot r} \][/tex]
