A circle has a center at (3 ,0 ) and passes through (0 ,1 ). What is the length of an arc covering (3pi ) /4 radians on the circle?

1 Answer
Feb 4, 2016

s ~~ 7.451

Explanation:

Arc length is computed using the formula s = r * theta

The center of the circle is on (3, 0) and it passes through (0, 1 ). Given these two points, we can determine the radius of the circle since we know that the radius is the distance from the center to any point on the circle.

[Solving for Radius]
Using the distance formula: sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)

d = sqrt((0-3)^2 + (1 - 0)^2)
d = sqrt((-3)^2 + (1)^2)
d = sqrt(9 + 1)
d = sqrt(10)

Using the arc length formula...

s = sqrt10 * (3pi)/4
s ~~ 7.451