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A circle with an arc length of ________ centimeters is intercepted by a central angle of 3pi/4 radians has a radius of ________ centimeters.

Blank1:
A) 12pi
B) 4pi
C) 2pi

Blank2:
A) 16
B) 24
C) 3

Respuesta :

InesWalston

Answer:

Blank1:   A) 12pi

Blank2:  A) 16

Step-by-step explanation:

We know that,

[tex]\text{Arc length}=\text{Radius }\times \text{Central angle (in rad)}=r\cdot \theta[/tex]

As given in the question, central angle is [tex]\dfrac{3\pi}{4}[/tex] radians

A-

Putting radius as 16 cm, we get

[tex]\text{Arc length}=16\cdot \dfrac{3\pi}{4}=12\pi[/tex]

B-

Putting radius as 24 cm, we get

[tex]\text{Arc length}=24\cdot \dfrac{3\pi}{4}=18\pi[/tex]

C-

Putting radius as 3 cm, we get

[tex]\text{Arc length}=3\cdot \dfrac{3\pi}{4}=\dfrac{9\pi}{4}[/tex]