Mr. Zheng is setting up a game of "capture the flag" for his P.E. class. The students will need to stay inside the bounds of a circular section that Mr. Zheng has roped off.
Mr. Zheng used
yards of rope to section off the playing field. What is the area, rounded to the nearest square yard, of the playing field for the "capture the flag" game?
Responses
A
square yards10 pi square yards
B
square yards 48 pi square yards
C
square yards144 pi square yards
D
576 pi square yards
To find the area of the circular playing field, we first need to calculate the radius of the circle.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Given that Mr. Zheng used 36 yards of rope to section off the playing field, we can plug that into the formula:
36 = 2πr
r = 18/π
r ≈ 5.73 yards
Now, we can calculate the area of the circular playing field using the formula A = πr^2:
A = π(5.73)^2
A ≈ 103.22 square yards
Rounded to the nearest square yard, the area of the playing field for the "capture the flag" game is 103 square yards.
Therefore, the answer is A) 10 pi square yards.