Question

An arc is intercepted by a central angle of 3π2 radians on a circle with a radius of 18 centimeters. What is the exact length of the arc? Enter your answer, in terms of π , in the box.

Answer 1

Answer:

The length of the arc is $27\pi \ cm$

Step-by-step explanation:

step 1

Find the circumference

we know that

The length of a complete circle is equal to the circumference of the circle

The circumference is equal to

$C=2\pi r$

we have

$r=18\ cm$

substitute

$C=2\pi (18)$

$C=36\pi\ cm$

step 2

we know that

A central angle of  $2\pi$ radians subtends the circumference of $36\pi\ cm$

so

by proportion

Find the length of the arc by a central angle of $\frac{3\pi }{2}$ radians

$\frac{36\pi }{2\pi}\frac{cm}{radians}=\frac{x}{(3\pi/2)}\frac{cm}{radians} \\ \\x=18*(3\pi/2)\\ \\x=27\pi \ cm$