Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the circle area A = 25π cm2 and Θ = π 4 . A) 20π cm B) …

Question

asked May 3, 2019 118k views

2 Answers

Chris Mitchelmore · Answer 1 · 2019-05-07T16:58:04+0000

Answer:

$L=(5\pi)/(4)$ cm

B is correct.

Explanation:

Use the fact that the length of an arc intercepted by an angle is proportional to the radius.

Area of circle
$=25\pi\text{ cm}^2$

$\theta=(\pi)/(4)$

$\theta=(l)/(r)$

$\pi r^2=25\pi\text{ cm}^2$

r=5

Put r and Ф into fact

$(\pi)/(4)=(l)/(5)$

$l=(5\pi)/(4)$

Hence, The length of arc is
$l=(5\pi)/(4)$ cm