The formula for the area of a circular sector is given by:

Area = 0.5 * r² * θ

where r is the radius of the circle and θ is the central angle in radians.

We are given that the area is 1,790 cm² and the central angle is 1.5 rad. We can substitute these values into the formula and solve for r:

1,790 = 0.5 * r² * 1.5

To isolate r², we divide both sides of the equation by 0.5 * 1.5:

r² = 1,790 / (0.5 * 1.5)

Solving for r² gives us:

r² = 2,387.33

Taking the square root of both sides to solve for r gives us:

r = √2,387.33

So, r ≈ 49 cm when rounded to the nearest centimeter.

Question

The formula for the area of a circular sector is given by:

Area = 0.5 * r² * θ

where r is the radius of the circle and θ is the central angle in radians.

We are given that the area is 1,790 cm² and the central angle is 1.5 rad. We can substitute these values into the formula and solve for r:

1,790 = 0.5 * r² * 1.5

To isolate r², we divide both sides of the equation by 0.5 * 1.5:

r² = 1,790 / (0.5 * 1.5)

Solving for r² gives us:

r² = 2,387.33

Taking the square root of both sides to solve for r gives us:

r = √2,387.33

So, r ≈ 49 cm when rounded to the nearest centimeter.

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