l asked in Science & MathematicsMathematics · 3 weeks ago

The radius of a given circle is 11 cm. Find the central angle (measured in radians) of a sector of the circle whose area is 250 cm2. ?

4 Answers

Relevance
  • 3 weeks ago

    Area is (1/2)r²θ....where r is the radius and θ is the central angle in radians.

    so, (1/2)(11)²θ = 250

    i.e. θ = 500/121 => 4.13 radians

    :)>

  • 3 weeks ago

    The radius of a given circle is 11 cm.

    Find the central angle (measured in radians) of a sector of the circle whose area is 250 cm^2.

    C = 2 pi 11

    and

    A = 121 pi = 380.132711 cm^2

    The central angle:

    250/380 (2 Pi) = 4.13367454 radians

  • 3 weeks ago

    The formula for the area of a sector is:

    A = ½ r² θ

    A : area (250 cm²)

    r : radius (11 cm)

    θ : central angle of the sector (in radians)

    250 = ½ (11²) θ

    500 = 121 θ

    θ = 500/121

    θ ≈ 4.13 radians

    Answer:

    About 4.13 radians

  • 3 weeks ago

    area of the circle is πr² = π11² = 121π cm²

    the sector is what percent of that

    As = 250/121π cm²

    that percent is the same percent of 2π radians, the full circle

    angle = 2π(250/121π) = 500/121 = 4.13 rad

Still have questions? Get your answers by asking now.