Question

Find the length of the given arc. (the bolded portion of the arc)

Answer 1

Answer:

Option D) 49π/4

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of the circle is equal to

$C=2\pi r$

where

r is the radius

we have

$r=7\ cm$

substitute

$C=2\pi(7)$

$C=14\pi\ cm$

step 2

Find the length of the given arc

we know that

The circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of the arc by a central angle of 315 degrees

Let

x ----> the length of the given arc

$\frac{14\pi}{360}=\frac{x}{315}\\\\x=14\pi(315)/360\\\\x=\frac{4,410\pi}{360}\ cm$

Simplify

$\frac{49\pi}{4}\ cm$