Question

A circle has a radius of 6 cm.

What is the exact length of an arc formed by a central angle measuring 45°?


4.5π cm

.75π cm

2.25π cm

1.5π cm

Answer 1

Yes I agree with the answer

Answer 2

`1.5\pi` cm

Explanation:

A central angle measuring
`45^\circ` is
`(45^\circ)/(360^\circ)=(45)/(360)`, or
`(1)/(8)` of the entire circle. The circumference of the circle is given by the formula
`2\pi r`, which is
`12\pi`.

Then, the length of an arc measuring
`(1)/(8)` of the entire circle is
`12\pi\cdot(1)/(8)=1.5\pi` cm.