Question

The circumference of the circle in the above figure is 128 ft. What is the length of AB?

A. 16 ft
B. 22.5 ft
C. 105.5 ft
D.45 ft

Answer 1

Answer: Option 'A' is correct.

Explanation:

Since we have given that

Circumference of circle = 128 ft

So, as we know the formula for "Circumference of circle":

`C=2\pi r=128\ ft`

We need to find the length of an arc AB.

As we know that the formula for "Length of an arc":

`Length=(\theta)/(360\textdegree)* 2\pi r\\\\L=(45\textdegree)/(360\textdegree)* 128\\\\Length=16\ ft`

Hence, Option 'A' is correct.

Answer 2

To answer this question, you should set up a proportion: central angle/360 = arc length/circumference where the central angle = 45 and circumference = 128 ft. After you cross multiply, you should find that the arc length of AB equals 16 ft, which is A.