Arc AB of circle O contgains 72 degree and is 6 pi long. Find area of circle O.
a. 9
b. 36
c. 30 pi
d. 225 pi
e. 900
please answer and explain
72 is 1/5 of 360, a full circle.
So, 5 * 6pi = 30pi and is the full circumference
since c = 2pi r, r = 15
since a = pi r^2, a = 225 pi
c = 2 pi r
30 = 2 pi r
r=15
a= pi r^2
= pi 25^2
= 225 pi
thank you
To find the area of the circle, we need to know the radius of the circle.
Given that arc AB contains 72 degrees and is 6π units long, we can use the formula for the circumference of a circle to find the radius.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Since the length of arc AB is 6π units, this means that the circumference of the circle is also 6π units.
Therefore, we can equate the circumference of the circle to 6π units:
2πr = 6π
Divide both sides of the equation by 2π:
r = 3
Now that we have the radius of the circle, we can calculate the area using the formula for the area of a circle, which is A = πr^2.
Substituting the value of the radius, we find:
A = π(3)^2
A = π(9)
A = 9π
Therefore, the area of circle O is 9π square units.
Comparing this result to the given options, we see that the correct answer is (c) 30π.