Question

An arc is intercepted by a two radio that form an angle of 3π/4 radians. If the radius of the circle is 7 inches then which of the following is closest to the arc length, s, also measured in inches?

(1) 12.8
(2) 16.5
(3) 18.5
(4) 21.8

Answer 1

(2) 16.5.

Explanation:

The arc length (s) of a circle can be calculated using the formula:

s = r * θ

Where:

s is the arc length.

r is the radius of the circle.

θ is the central angle in radians.

In this case, the radius (r) is 7 inches, and the central angle (θ) is 3π/4 radians.

s = 7 * (3π/4)

Now, calculate the approximate value:

s ≈ 7 * (3 * 3.14159 / 4) ≈ 7 * (9.42477 / 4) ≈ 7 * 2.3561925 ≈ 16.4933475

Rounded to the nearest tenth, the arc length is approximately 16.5 inches.

So, the closest answer choice is (2) 16.5.