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The length of arc PR is 12 centimeters and its measure is 60° on circle O.Section A:A. 68.76B. 275.06C. 137.51Section B:A. 57.86B. 34.92C. 82.90

The length of arc PR is 12 centimeters and its measure is 60° on circle O.Section-example-1
User Arabella
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1 Answer

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The length l of the arc is calculated below as


\begin{gathered} l=(\theta)/(360)*2\pi r \\ Substitute\text{ }\theta=60^0\text{ and }l=12\text{ into the equation:} \\ 12=(60)/(360)*2\pi* r \end{gathered}

Therefore, the value of r:


r=11.46

To find the area, A, of a sector, the formula is


\begin{gathered} A=(\theta)/(360)*\pi r^2 \\ Where\text{ } \\ r=11.46\text{ cm \lparen two decimal places\rparen} \end{gathered}

Substitute for r


\begin{gathered} A=(60)/(360)*\pi*(11.46)^2 \\ A=68.76\text{ cm}^2\text{ } \end{gathered}

Hence,

The area of the sector is approximately is 68.76cm²

The perimeter of the sector is given by:


length\text{ of arc}+r+r

Therefore, the perimeter is given by:


12+2*11.4615\approx34.92cm

Hence,

The perimeter of the sector is approximately 34.92cm

User Rodrigobb
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