Question

For a circle of radius 5 feet, find the arc length "s" cut off by a central angle of 18°.

A) 90π feet
B) 3/2π feet
C) 1/2π feet
D) π feet

Answer 1

The arc length 's' for a circle with a radius of 5 feet cut by a central angle of 18° is 1/2π feet. This is calculated by taking the full circumference (10π feet) and multiplying it by the fraction of the circle that corresponds to the angle (1/20).

Step-by-step explanation:

To find the arc length 's' cut off by a central angle of 18° for a circle of radius 5 feet, we first recognize that the circumference for a full circle (360°) is given by the formula 2πr. Knowing that, we can calculate the proportion of the circumference that corresponds to an 18° angle by setting up a ratio, since the degrees in a circle and the arc length are directly proportional.

For an 18° angle in a circle of radius 5 feet, the arc length 's' is obtained by:

1. Finding the full circumference with the formula C = 2πr, where r is the radius.
2. Since r = 5 feet, C = 2π × 5 feet = 10π feet.
3. Next, we find the fraction of the circumference that corresponds to 18° out of 360°, or 18/360.
4. Finally, we multiply the full circumference by the fraction (18/360), which simplifies to 1/20.
5. Therefore, the arc length 's' is 10π feet × 1/20 = 1/2π feet, which matches answer option (C).