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

Question

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Mathematics

Answered

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 :

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calculista calculista · Answer 1 · 2025-03-23T13:51:55-04:00

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

[tex]C=2\pi r[/tex]

where

r is the radius

we have

[tex]r=7\ cm[/tex]

substitute

[tex]C=2\pi(7)[/tex]

[tex]C=14\pi\ cm[/tex]

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

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

Simplify

[tex]\frac{49\pi}{4}\ cm[/tex]

Find the length of the given arc. (the bolded portion of the arc)A) 343π/8 cmB)49π C) 45π/8D) 49π/4

Answer :

Other Questions

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