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I would like some help with these please

Answer»

In terms of π

Arc AB = 0.83 π metres

Arc DE = 2.5 π metres

Arc GH = 1.6 π metres

Explanation →

Given ,

  • Three circles of RADIUSES 1m , 3m and 2m.
  • R1 = 1m
  • R2 = 3m
  • R3 = 2m

  • The angle ( ∅ ) is given as = 150° for each CIRCLE

So , Calculating the Arc lengths of each circle by using the FORMULA ,

  • Arc Length = 2πr ( ∅ / 360° )

For 1st circle having radius R1 = 1m , Arc length will be ,

  • Arc length ( AB ) = 2π R1 ( ∅ ÷ 360° )
  • AB = 2π x 1 x 150° / 360°
  • AB = 300° / 360° x π
  • AB = 0.83 π m ( in terms of π )

For 2nd circle having radius R2 = 3m , Arc length will be ,

  • Arc length ( DE ) = 2π R2 ( ∅ ÷ 360° )
  • DE = 2π x 3 x 150° / 360°
  • DE = 900° / 360° x π
  • DE = 2.5 π m ( in terms of π )

For 3rd circle having radius R2 = 2m , Arc length will be ,

  • Arc length ( GH ) = 2π R3 ( ∅ ÷ 360° )
  • GH = 2π x 2 x 150° / 360°
  • GH = 600° / 360° x π
  • GH = 1.6 π m ( in terms of π )

\rule{200}{4}

Length of arc

  • AB = 0.83 x π
  • AB = 2.619047 metres

Length of arc

  • DE = 2.5 x π
  • DE = 7.857142 metres

Length of arc

  • GH = 1.6 x π
  • GH = 5.23809 metres

\rule{200}{4}


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