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Area of sector

[tex]\\ \rm\Rrightarrow \dfrac{\theta}{360}\pi r^2[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{150}{360}\pi (4)²[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5}{12}\pi (16)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5}{3}\pi(4)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{20\pi}{3}[/tex]

[tex]\\ \rm\Rrightarrow 20.9cm²[/tex]

SenorMathWiz

Answer:

20.9

Step-by-step explanation:

area of a sector of a circle = (Ф/360) × πr²

where Ф = central angle of sector and r = radius

here the sector has a central angle of 150° and a radius of 4

so Ф = 150 and r = 4

we have A = (Ф/360) × πr²

==> plug in Ф = 150 and r = 4

A = (150/360) × π(4)²

==> evaluate the exponent

A = (150/360) × 16π

==> simplify 16π

A = (150/360) × 50.3

==> multiply 150/360 by 50.3

A = 20.9

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