Question

GEOMETRY)

Find the area in square miles, of the sector shown below. Round your answer to the nearest whole number. (Enter only a number for your answer.)

(Picture is below) Thank you!

Answer 1

SOLUTION :-

AREA of sector = ( ∆/360° ) × πr²

∆ = given angle , r = radius

hence ,

AREA of sector for given angle

= ( 120°/360° ) × π 12² mi²

= ⅓ × π × 144 = 150.79 mi² = 151 mi² ( rounded off )

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Answer 2

Answer:

Sector area = 151 mi²

Step-by-step explanation:

We can use the formula for sector area:

Area = $\frac{\theta}{360} \pi\ r^2$

where:
θ = central angle (120°),

r = radius of circle (12 mi) .

Substituting these values into the formula:

Area = $\frac{120}{360} \pi\ \times (12)^2$

        ⇒ 48 π

        ⇒ 150.796

        ≈  151 mi²   (rounded to the nearest whole number)