1) If a circle sector has a radius of 5 cm and a central angle of 3 radians, then the arc length of the sector is 15 cm. True or False?

2) If a circle sector has a radius of 6 cm and a central angle of 240 degrees, then the arc length of the sector is 8 (pi) cm. True or False?

The answer is true. use arc length = (centeral angle/2π) 2πr

we know that the circumference of a circle is equal to 2πr. That means when we have 2π radians out of 2π radians (one hundred percent of the circle). If we are only dealing with part of the circle (sector), you find what percent of the complete circle the sector is by dividing the central angle by 2π. In this case we have 3 radians out of 2π radians, therefore we only have 47.75% of the circle. Because we only have a certain percentage of the circle, you multiply 2πr by the percent to get the arc length given by the sector. In this case 0.4775x2xπx5 which equals 15.001 which is rounded down to 15 cm. Therefore the answer is true.