Question

14. Find the length of the arc with the properties below in

terms of pi.
Radius = 12 ft
Degrees = 225°
A) 90 π ft
B) 19π ft
C) 15π ft
10
D) ft
T π
3

Answer 1

To find the arc length with a radius of 12 ft and 225°, we calculate ⅓ of the circle's circumference (2×pi×r). Multiplying the values gives us an arc length of 15pi ft, thus the correct answer is 15pi ft (option C).

Step-by-step explanation:

To find the length of the arc with a radius of 12 ft and a central angle of 225°, we need to use the formula for the arc length of a circle, which is:

Arc length = (Central Angle in Radians / 360°) × 2×pi× Radius

First, we have to convert degrees to radians.

Since 225° is ⅓ of a full circle (360°), we can also say it is ⅓ of the full circle's circumference. Therefore, the formula becomes:

Arc length = ⅓ × 2×pi× 12 ft

Multiplying the values we get:
Arc length = 0.625 × 2×pi× 12 ft

= 15pi ft

Answer: The length of the arc in terms of pi is 15pi ft, which corresponds to option C).