solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument? the circumference of a circle is given by the formula c=pi d , where d is the diameter. because the diameter is twice the radius, c= 2 pi r. if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to 360°/n° the arc length of each sector is the circumference divided by the number of sectors, or _____. therefore, the arc length of a sector of a circle with a central angle of n° is given by 2pirn/360 or pirn/180 . a. 2pir/270/n b. 2pir/360/n c. 2pir/180/n d. 2pir/90/n

the numbers of sectors is 360/n

Then, the arc length is the circumference divided by 360/n which is the same that the circumference times n/360

So, the arc length is 2pir/(360/n), which is the option b.

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ColinJacobus ColinJacobus · Answer 2 · 2019-01-11T03:01:28-05:00

Answer: The answer is (b). \(\dfrac{2\pi r}{\frac{360^\circ}{n^\circ}}.\)

Step-by-step explanation: Let us consider a circle with centre "O" and radius OA=OB=r units. We know that the circumference of a circle is \(2\pi\times radius~of~the~circle,\) so the circumference of Circle 'C' is given by

\(Circumference=2\pi r.\)

Also, let us central angles of equal size of 'n°', the the number of sectors formed is given by

\(no.~of~sectors=\dfrac{360^\circ}{n^\circ}.\)

Now, the formula for arc length of a sector is given by

\(arc~length~of~of~a~sector=\dfrac{Circumference~of~the~circle}{no.~of~equally~sized~sectors}.\)

∴ \(arc~length~of~of~a~sector=\dfrac{2\pi r}{\frac{360^\circ}{n^\circ}}.\)

Thus, (b) is the correct option.