Question

i would like some help with these please

Answer 1

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

$\rule{200}{4}$