Question

A central angle of a circle measures 1.5 radians. If the radius of the circle is 3 cm, what is the area of the related sector?

A) 4.55 cm2
B) 6.75 cm2
C) 7.38 cm2
D) 8.24 cm2

Answer 1

Option B.
`6.75\ cm^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=3\ cm`

substitute

`A=\pi (3^(2))=9 \pi\ cm^(2)`

Remember that

`2\pi` radians subtends the complete circle of area
`9 \pi\ cm^(2)`

so

by proportion

Find the area of the related sector for a central angle of
`1.5` radians

Let

x------> the area of the related sector

`(9 \pi)/(2\pi)(cm^(2))/(radians) =(x)/(1.5)(cm^(2))/(radians)\\ \\x=9*1.5/2\\ \\x= 6.75\ cm^(2)`