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Finding the radius of a circle when given the arc length and angle of a sector of the circle.

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If the arc length for a sector of a circle is $\\var{s}$ cm with an angle $\\theta=\\frac{\\pi}{\\var{t}}$ radians, calculate the radius of the circle.

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If we have the arc length and central angle for a sector of a circle, to calculate the radius of the circle we want to use the formula \\[ s = r \\theta \\implies r = \\frac{s}{\\theta} \\]

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where $s$ is the arc length, $r$ is the radius of the circle, and $\\theta$ is the central angle measured in radians:

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{geogebra_applet('https://www.geogebra.org/m/pbds8nkd')}

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So, if $s=\\var{s}$ cm and $\\theta=\\frac{\\pi}{\\var{t}}$, then

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\\[ \\begin{split} r &\\,= \\frac{\\var{s}}{\\frac{\\pi}{\\var{t}}} \\text{ cm} \\\\ \\\\&\\,= \\simplify[all, fractionNumbers]{{s*t}/pi} \\text{ cm} \\\\ &\\,= \\var{r2} \\text{ cm (2 d.p.)} \\end{split} \\]

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$r=$[[0]] cm

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(Give your answer to 2 decimal places where necessary.)

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