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 ci
rcle area A = 25π cm2 and Θ = π 4 . A) 20π cm B) 5π 4 cm C) 4π 5 cm D) 10π 4 cm
2 answers:
The answer is definetly b 5 pi 4 cm
Answer:
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](https://tex.z-dn.net/?f=%3D25%5Cpi%5Ctext%7B%20cm%7D%5E2)
![\theta=\dfrac{\pi}{4}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cdfrac%7B%5Cpi%7D%7B4%7D)
![\theta=\dfrac{l}{r}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cdfrac%7Bl%7D%7Br%7D)
![\pi r^2=25\pi\text{ cm}^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%3D25%5Cpi%5Ctext%7B%20cm%7D%5E2)
![r=5](https://tex.z-dn.net/?f=r%3D5)
Put r and Ф into fact
![\dfrac{\pi}{4}=\dfrac{l}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpi%7D%7B4%7D%3D%5Cdfrac%7Bl%7D%7B5%7D)
![l=\dfrac{5\pi}{4}](https://tex.z-dn.net/?f=l%3D%5Cdfrac%7B5%5Cpi%7D%7B4%7D)
Hence, The length of arc is
cm
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