find the length of an arc of a circle whose circumference is 832.38 cm and central angle is 333 degrees

1 answer

First, we need to find the circumference of the entire circle, since we only have the value for the circumference given. We know that the circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. We can rearrange this formula to solve for the radius, r = C/2π.

r = 832.38 cm / (2 x 3.14159) = 132.53 cm

Now that we know the radius, we can use the central angle and the formula for the length of an arc of a circle to find the length of the arc. The formula for the length of an arc of a circle is given by L = (central angle/360) x 2πr.

L = (333/360) x (2 x 3.14159) x 132.53 cm
L = 1.03 x 835.15
L = 859.01 cm

Therefore, the length of the arc is approximately 859.01 cm.