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

`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