Question

There are two concentric circles. The smaller circle has a radius of 8 cm and the larger circle has a radius of 12 cm. A central angle forms an arc on both circles. If the length of the arc on the smaller circle is 17 cm, then what is the length of the arc on the larger circle?

A. 25.5 cm
B. 5.6 cm
C. 11.3 cm
D. 17.7 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the arc on the larger circle, we can use the formula:

Arc Length = radius x angle in radians

First, we need to find the angle in radians for both circles.

For the smaller circle:
Arc Length = 17 cm
Radius = 8 cm
Angle in radians = Arc Length / Radius = 17 cm / 8 cm ≈ 2.125 radians

Now, we can use the angle in radians to find the length of the arc on the larger circle:
Radius = 12 cm
Angle in radians = 2.125 radians
Arc Length = 12 cm x 2.125 ≈ 25.5 cm

Therefore, the length of the arc on the larger circle is 25.5 cm, which corresponds to option A.