Respuesta :

Answer:

  1. 150π ft²
  2. 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.

elvokipkorir

Answer:

1. 150π ft²

2. 10π ft²

Step-by-step explanation:

Hello there!

Here is how we solve the given problem:

  1. 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.
  2. 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;

  1. A = (∆°/360°) × πr²
  2. L = ∆°/360° × 2πr.

I hope this helps.

Have a nice studies. :)

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