Question

A sector of a circle of radius 80 mi has an area of 1600 mi2. Find the central angle (in radians) of the sector.

Answer 1

Answer:

The central angle of the sector is 0.5 radian

Step-by-step explanation:

given;

radius of the circle, r = 80 mi

area of the sector, A = 1600 mi²

Area of sector is given by;

A = ¹/₂r²θ

where;

θ is the central angle (in radians) of the sector

$\theta = \frac{2A}{r^2}\\\\\theta = \frac{2*1600}{80^2}\\\\ \theta = 0.5 \ radian$

Therefore, the central angle of the sector is 0.5 radian

Answer 2

The central angle (in radians) of the sector is 28.66 degrees

The formula for calculating the area of a sector is expressed as:

$A = \theta/360 \times \pi r^2$

Given the following parameters

radius r = 80mi

Area of sector A = 1600mi²

Substitute the given parameters into the formula

1600 = Ф/360 * (3.14)(80)²

1600 * 360 = 20,096Ф

Ф = 576000/20,096

Ф =28.66 degrees

Hence the central angle (in radians) of the sector is 28.66 degrees

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