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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]

We are given that the area [tex]$A$[/tex] is [tex]$38.5\,\text{cm}^2$[/tex] and that [tex]$\pi = \frac{22}{7}$[/tex]. To find the radius [tex]$r$[/tex], we start by solving for [tex]$r^2$[/tex]:

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

Dividing by a fraction is the same as multiplying by its reciprocal, so

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

Calculating the product,

[tex]$$
38.5 \times \frac{7}{22} = 12.25.
$$[/tex]

Now, take the square root of both sides to find [tex]$r$[/tex]:

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

Thus, the radius of the circle is [tex]$3.5$[/tex] cm.

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