21.8k views
5 votes
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

1 Answer

6 votes

Answer:

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)

User Gearhead
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories