The radius of a sector of a certain circle is three times the radius of a smaller circle.If the perimeter of the sector is the same as the circumference of the smaller circle, find the angle of the sector. (Give your answer correct to 3 significant figures.)
(Need the solution and steps)
Circumference and Area
2015-05-22 3:12 am
回答 (1)
2015-05-22 4:26 am
✔ 最佳答案
Let the radius of the smaller circle be r, the angle of the sector be θ.The perimeter of the sector
= 3r + 3r + 3r × 2π × θ/360°
= r × (6 + θπ/60°)
The perimeter of the smaller circle
= 2πr
⇒ r × (6 + θπ/60°) = 2πr
6 + θπ/60° = 2π
θ = 60° × (2π - 6)/π
θ = 5.41°
∴ The angle of the sector is 5.41°.
收錄日期: 2021-04-20 15:35:45
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