What is the arc length of the arc (AB) shown in the figure?
12cm
45^o
The arc length of arc AB can be found using the formula:
arc length = (angle/360) x 2πr
where r is the radius of the circle.
Since we are not given the radius of the circle, we cannot directly use this formula. However, we can use the fact that the angle of the arc is 45 degrees and the circumference of a full circle with radius r is 2πr.
If the whole circle has a circumference of 2πr, then 45 degrees (or 1/8 of the circle) has an arc length of:
arc length = (1/8) x 2πr = πr/4
Therefore, we just need to know the radius of the circle to find the arc length. However, without more information, we cannot determine the radius or the arc length. So the answer is: There is not enough information to calculate the arc length of arc AB.
To find the arc length of an arc (AB), you can use the formula:
Arc Length = (Angle / 360) x (2πr)
Given:
Angle (θ) = 45°
Radius (r) = 12 cm
Using the formula, we can substitute the values:
Arc Length = (45° / 360°) x (2π x 12 cm)
Simplifying the equation:
Arc Length = (1/8) x (24π cm)
Arc Length = 3π cm or approximately 9.42 cm
Therefore, the arc length of the arc (AB) is 3π cm or approximately 9.42 cm.