Mathematics
Grade9
Easy

Question

Find the perimeter of the sector PQR shown below

  1. 132 cm    
  2. 142 cm    
  3. 128 cm    
  4. 156 cm    

hintHint:

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 andpi 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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