Answer:
Exact answer: [tex]27\pi[/tex]
Answer rounded to nearest hundredths: 84.82 using the pi button and not 3.14.
Step-by-step explanation:
Let's pretend for a second the whole circle is there.
The area of the circle would be [tex]A=\pi r^2[/tex] where [tex]r=6[/tex] since 6 cm is the length of the radius.
So the area of the full circle would have been [tex]A=\pi \cdot 6^2[/tex].
[tex]A=\pi \cdot 6^2[/tex]
Simplifying the 6^2 part gives us:
[tex]A=\pi \cdot 36[/tex]
or
[tex]A=36 \pi[/tex]
Now you actually have one-fourth (because of the 90 degree angle located at the central angle) of the circle missing so our answer is three-fourths of what we got from finding the area of the full circle.
So finding three-fourths of our answer means taking the [tex]36\pi[/tex] we got earlier and multiplying it by 3/4.
This means the answer is [tex]\frac{3}{4} \cdot 36\pi[/tex].
3/4 (36)=3(9)=27
So the answer is [tex]27\pi[/tex]
