Answer:
see explanation
Step-by-step explanation:
arc length (l) is calculated as
• l = circumference of circle × fraction of circle
the area of a sector (A) is calculated as
• A = area of circle × fraction of circle
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Using these formulae to calculate the given questions.
(1)
l = 2πr × [tex]\frac{40}{360}[/tex] ( r is the radius )
= 2π × 3 × [tex]\frac{4}{36}[/tex]
= 6π × [tex]\frac{1}{9}[/tex]
= π × [tex]\frac{6}{9}[/tex]
= π × [tex]\frac{2}{3}[/tex] ≈ 2.09 9n ( to 2 decimal places )
A = πr² × [tex]\frac{40}{360}[/tex]
= π × 3² × [tex]\frac{1}{9}[/tex]
= 9π × [tex]\frac{1}{9}[/tex] = π ≈ 3.14 in² ( to 2 decimal places )
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(2)
l = 2πr × [tex]\frac{240}{360}[/tex]
= 2π × 6 × [tex]\frac{2}{3}[/tex]
= 12π × [tex]\frac{2}{3}[/tex]
= 8π ≈ 25.13 yd ( to 2 decimal places )
A = πr² × [tex]\frac{2}{3}[/tex]
= π × 6² × [tex]\frac{2}{3}[/tex]
= 36π × [tex]\frac{2}{3}[/tex]
= 24π ≈ 75.40 yd² ( to 2 decimal places )
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(3)
l = 2πr × [tex]\frac{135}{360}[/tex]
given diameter = 8, then r = 8 ÷ 2 = 4 , then
l = 2π × 4 × [tex]\frac{3}{8}[/tex]
= 8π × [tex]\frac{3}{8}[/tex]
= 3π
≈ 9.42 cm ( to 2 decimal places )
A = πr² × [tex]\frac{3}{8}[/tex]
= π × 4² × [tex]\frac{3}{8}[/tex]
= 16π × [tex]\frac{3}{8}[/tex]
= 6π
≈ 18.85 cm² ( to 2 decimal places )
