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The area of a circle is [tex]$38.5 \, \text{cm}^2$[/tex]. Find the length of the radius of the circle. (Take [tex]\pi = \frac{22}{7}[/tex]).

Answer :

The area of a circle is given by the formula

[tex]$$
A = \pi r^2.
$$[/tex]

Given that the area is [tex]$38.5\text{ cm}^2$[/tex] and [tex]$\pi = \frac{22}{7}$[/tex], we substitute these into the formula:

[tex]$$
38.5 = \frac{22}{7}r^2.
$$[/tex]

To solve for [tex]$r^2$[/tex], multiply both sides by [tex]$\frac{7}{22}$[/tex]:

[tex]$$
r^2 = 38.5 \times \frac{7}{22}.
$$[/tex]

Calculating the above expression gives:

[tex]$$
r^2 = 12.25.
$$[/tex]

Taking the square root of both sides:

[tex]$$
r = \sqrt{12.25} = 3.5.
$$[/tex]

Thus, the length of the radius of the circle is [tex]$3.5\text{ cm}$[/tex].

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