High School

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------------------------------------------------ Find the area of a sector of a circle with radius [tex]r = 15.0 \, \text{m}[/tex] and central angle [tex]\theta = 20^\circ[/tex]. If necessary, express the answer to the nearest tenth.

A) [tex]2.6 \, \text{m}^2[/tex]

B) [tex]0.5 \, \text{m}^2[/tex]

C) [tex]39.3 \, \text{m}^2[/tex]

D) [tex]78.5 \, \text{m}^2[/tex]

Answer :

Rounding the answer to the nearest tenth, the area of the sector is approximately 6.2 m² that is option A.

To find the area of a sector of a circle, you can use the formula:

Area = (θ/360) * π * r²

Where θ is the central angle in degrees, π is a constant approximately equal to 3.14159, and r is the radius of the circle.

In this case, the radius is given as 15.0 m and the central angle is 20°.

Substituting these values into the formula, we have:

[tex]Area = (20/360) * π * (15.0)^2[/tex]

Calculating this expression, we get:

Area ≈ 0.087 * 3.14159 * 225

Area ≈ 6.15897 m²

Rounding the answer to the nearest tenth, the area of the sector is approximately 6.2 m².

Therefore, the correct answer is A) 2.6 m².

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