Question

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

Answer 1

Answer:

Blank1:   A) 12pi

Blank2:  A) 16

Step-by-step explanation:

We know that,

$\text{Arc length}=\text{Radius }\times \text{Central angle (in rad)}=r\cdot \theta$

As given in the question, central angle is $\dfrac{3\pi}{4}$ radians

A-

Putting radius as 16 cm, we get

$\text{Arc length}=16\cdot \dfrac{3\pi}{4}=12\pi$

B-

Putting radius as 24 cm, we get

$\text{Arc length}=24\cdot \dfrac{3\pi}{4}=18\pi$

C-

Putting radius as 3 cm, we get

$\text{Arc length}=3\cdot \dfrac{3\pi}{4}=\dfrac{9\pi}{4}$