SOLUTION: A circle has an area of 25 pi and is divided into 8 congruent regions. What is the perimeter of one of these regions? a) 10 - 25pi b) 10 + 5/8pi c) 10 + 5/4pi d) 10 + 5pi e)

Algebra ->  Circles -> SOLUTION: A circle has an area of 25 pi and is divided into 8 congruent regions. What is the perimeter of one of these regions? a) 10 - 25pi b) 10 + 5/8pi c) 10 + 5/4pi d) 10 + 5pi e)       Log On


   

Question 312031: A circle has an area of 25 pi and is divided into 8 congruent regions. What is the perimeter of one of these regions?
a) 10 - 25pi
b) 10 + 5/8pi
c) 10 + 5/4pi
d) 10 + 5pi
e) 10 + 25pi
If possible can you please explain how you came up with the answer?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of the region is made up of the circular portion plus two radii (think of a pie piece). You can calculate the circular portion because you know for the whole circle that the entire circular portion would be the circumference.
C=2%2Api%2AR
If the circle is divided into 8 parts, then the circular portion of the perimeter of each pie slice would be %281%2F8%29C=%28pi%2F4%29R
Then adding the two radii, the perimeter would be,
P=2R%2B%28pi%2F4%29R.
.
.
.
Now finding R.
You know the area of the circle, the equation for the area is,
A=pi%2AR%5E2=25%2Api
R%5E2=25
R=5
Now go back and plug this value into the perimeter equation,
P=2R%2B%28pi%2F4%29R
P=2%285%29%2B%28pi%2F4%29%285%29
highlight_green%28P=10%2B%285%2F4%29%2Api%29
c) is the correct answer.