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

Blank1: A) 12pi

Blank2: A) 16

Explanation:

We know that,

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

As given in the question, central angle is
`(3\pi)/(4)` radians

A-

Putting radius as 16 cm, we get

`\text{Arc length}=16\cdot (3\pi)/(4)=12\pi`

B-

Putting radius as 24 cm, we get

`\text{Arc length}=24\cdot (3\pi)/(4)=18\pi`

C-

Putting radius as 3 cm, we get

`\text{Arc length}=3\cdot (3\pi)/(4)=(9\pi)/(4)`