Answered

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The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?

Give the exact answer in simplest form.

____ square kilometers. (pi, fraction,)​

The Radius Of A Circle Is 6 Kilometers What Is The Area Of A Sector Bounded By A 126 ArcGive The Exact Answer In Simplest Form Square Kilometers Pi Fraction class=

Sagot :

Corsaquix

Answer:

[tex]12.6\pi\:\mathrm{km^2}\:\text{or }\frac{63}{5}\pi\:\mathrm{km^2}[/tex]

Step-by-step explanation:

The area of a sector with measure [tex]\theta[/tex] in degrees is given by [tex]r^2\pi\cdot\frac{\theta}{360}[/tex], where [tex]r[/tex] is the radius of the sector.

What we're given:

  • [tex]r[/tex] of 6
  • [tex]\theta[/tex] of [tex]126^{\circ}[/tex]

Substituting given values, we get:

[tex]A_{sec}=6^2\pi \cdot\frac{126}{360}=\boxed{12.6\pi\:\mathrm{km^2}}[/tex]

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