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Sagot :
Answer:
- 150π ft²
- 10π ft.
Step-by-step explanation:
Area of the sector :
[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
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Length of the arc :
[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.
Answer:
1. 150π ft²
2. 10π ft²
Step-by-step explanation:
Hello there!
Here is how we solve the given problem:
- Area of the sector of a circle refers to the fractional circle area. Which is given by; (∆°/360°) × πr². Where ∆° is the angle subtended by the arc.
- the arc length also refers to the length swept by the arc with angle theta (∆°) - subtended. Given by
L = ∆°/360° ×2πr
From our problem,
∆ = 60°, r = 30ft
Lets substitute the values
1. A = (∆°/360°) × πr²
= 60°/360° × π × 30²
= 150π ft²
2. L = ∆°/360° × 2πr
= (60/360) × 2 × 30 × π
= 10π ft²
NOTE:
Use the formulas given below to be on a save side;
- A = (∆°/360°) × πr²
- L = ∆°/360° × 2πr.
I hope this helps.
Have a nice studies. :)
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