Pamelacoleviz
Answered

In a circle with radius 2cm, a sector has an area πcm². what is the measure of the arc of the sector? ​

Sagot :

AGboiiviz

Answer:

The answer is π

Step-by-step explanation:

Formula

  • Area of a sector= (θ/360)πr²
  • Arc length = 2πr(θ/360)

Given:

  • Area = πcm²
  • r = 2cm
  • θ = ?

Plugging the values to find the central angle

  • Area of a sector= (θ/360)πr²
  • πcm² = (θ/360)π(2cm)²
  • πcm² = (θ/360)(4πcm²)

cancel πcm²

  • 1 = (θ/360)(4)
  • 1 = (4θ/360)
  • 1 = (θ/90)
  • 1×90 = θ
  • 90 = θ

Hence , the central angle is 90°

Now , we plug again the values to get the arc length

  • Arc length = 2πr(θ/360)
  • Arc length = 2π(2)(90/360)
  • Arc length = 4π(1/4)
  • Arc length = 4π/4
  • Arc length = π

Therefore , the measure of the arc of the sector is π