58 shrubs are needed
Step-by-step explanation:
Laura garden is shaped like a circle sector with
- A radius 62 feet
- A central angle 47°
- Shrubs are planted every 3 feet along the border of the garden
We need to find how many shrubs are needed
The formula of length an arc = [tex]\frac{\alpha }{360}*2\pi r[/tex] ,
where α is the central angle and r is the radius of the sector
Look to the attached figure
The border of the garden is the perimeter of the circular sector
The perimeter of the sector = r + r + length the arc
∵ The radius of the sector is 62 feet
∵ The measure of the central angle is 47°
∴ The length of the arc = [tex]\frac{47}{360}*2\pi (62)[/tex]
∴ The length of the arc = 50.86 feet
∵ The perimeter of the sector = r + r + length the arc
∴ The perimeter of the sector = 62 + 62 + 50.86
∴ The perimeter of the sector = 174.86 feet
∵ Shrubs are planted every 3 feet along the border of the garden
∵ The length of the border of the garden is 174.86 feet
- Divide the length of the border by 3 to find the number of shrubs
∵ 174.86 ÷ 3 = 58.28
∴ The number of shrubs is 58
58 shrubs are needed
Learn more:
You can learn more about the circular sector in brainly.com/question/10610299
#LearnwithBrainly
