Question

A circle has a radius of 8ft. Find the length s of the arc intercepted by a central angle of π3 radians. Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

Answer:

8.4ft

Step-by-step explanation:

Formula for calculating the length of an arc is expressed as $L = \frac{\theta}{360} * 2\pi r$

$\theta$ is the central angle = π/3 rad

r is the radius of the circle = 8ft

Substituting the values into the formula above we have;

$L =$ $\frac{(\frac{\pi}{3} )}{2 \pi} * 2\pi (8)$

$L = \frac{\pi}{6 \pi} * 2\pi(8) \\\\L = 1/6 * 16\pi\\\\L = 8\pi/3\\\\L = \frac{8(22/7)}{3} \\\\L = \frac{8*22}{7*3}\\ \\L = 176/21\\\\L = 8.4 ft (to\ the\ nearest\ tenth)$

Hence, the length of the arc s is approximately 8.4 ft.