Question

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

A)

343π/8 cm

B)49π

C)

45π/8

D)

49π/4

Answer 1

Option D) 49π/4

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

`(14\pi)/(360)=(x)/(315)\\\\x=14\pi(315)/360\\\\x=(4,410\pi)/(360)\ cm`

Simplify

`(49\pi)/(4)\ cm`