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Mathematics

Grade9

Easy

Question

Find the perimeter of the sector PQR shown below

132 cm
142 cm
128 cm
156 cm

hint Hint:

$I equals fraction numerator theta over denominator 360 to the power of ring operator end exponent end fraction cross times 2 pi r$

The correct answer is: 128 cm

Length of the arc is
$I equals fraction numerator theta over denominator 360 to the power of ring operator end exponent end fraction cross times 2 pi r$
Substitute $theta equals 60 to the power of ring operator end exponent comma r equals 42$ and $pi equals fraction numerator 22 over denominator 7 end fraction$ .
$I equals fraction numerator 60 to the power of ring operator end exponent over denominator 360 to the power of ring operator end exponent end fraction cross times 2 cross times fraction numerator 22 over denominator 7 end fraction cross times 42$
$I equals fraction numerator 1 over denominator 6 end fraction cross times 2 cross times 22 cross times 6$
I=1×2×22
I=44 cm
Perimeter of sector is=I+2r
Substitute ∣=44 and r=42.
=44+2(42)
=44+84
=128 cm

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