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A circle has a radius of 6 cm.

What is the exact length of an arc formed by a central angle measuring 45°?


4.5π cm

.75π cm

2.25π cm

1.5π cm

Sagot :

Answer:

[tex]1.5\pi[/tex] cm

Step-by-step explanation:

A central angle measuring [tex]45^\circ[/tex] is [tex]\frac{45^\circ}{360^\circ}=\frac{45}{360}[/tex], or [tex]\frac{1}{8}[/tex] of the entire circle. The circumference of the circle is given by the formula [tex]2\pi r[/tex], which is [tex]12\pi[/tex].

Then, the length of an arc measuring [tex]\frac{1}{8}[/tex] of the entire circle is [tex]12\pi\cdot\frac{1}{8}=1.5\pi[/tex] cm.

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