Question

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) 5π 4 cm C) 4π 5 cm D) 10π 4 cm

Answer 1

the answer is definetly b 5 pi 4 cm

Answer 2

Answer:

$L=\dfrac{5\pi}{4}$ cm

B is correct.

Step-by-step explanation:

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

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

$\theta=\dfrac{\pi}{4}$

$\theta=\dfrac{l}{r}$

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

$r=5$

Put r and Ф into fact

$\dfrac{\pi}{4}=\dfrac{l}{5}$

$l=\dfrac{5\pi}{4}$

Hence, The length of arc is $l=\dfrac{5\pi}{4}$ cm