To calculate the radius of a circle given its area, we start with the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Where [tex]\( A \)[/tex] is the area, [tex]\( \pi \)[/tex] is a constant, and [tex]\( r \)[/tex] is the radius. Given the area [tex]\( A = 154 \, \text{cm}^2 \)[/tex] and [tex]\( \pi = \frac{22}{7} \)[/tex], we need to solve for [tex]\( r \)[/tex].
First, we substitute the given values into the area formula:
[tex]\[ 154 = \left(\frac{22}{7}\right) r^2 \][/tex]
Next, we solve for [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = \frac{154}{\frac{22}{7}} \][/tex]
To simplify the right-hand side, we multiply by the reciprocal of [tex]\(\frac{22}{7}\)[/tex]:
[tex]\[ r^2 = 154 \times \frac{7}{22} \][/tex]
Now, we simplify the multiplication:
[tex]\[ r^2 = \frac{154 \times 7}{22} \][/tex]
[tex]\[ r^2 = \frac{1078}{22} \][/tex]
[tex]\[ r^2 = 49 \][/tex]
To find the radius [tex]\( r \)[/tex], we take the square root of both sides:
[tex]\[ r = \sqrt{49} \][/tex]
[tex]\[ r = 7 \][/tex]
Therefore, the radius of the circle is:
[tex]\[ \boxed{7 \, \text{cm}} \][/tex]
