Answer :

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]

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