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. ?
- Wayne DeguManLv 78 months 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
- KrishnamurthyLv 78 months 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
A = 121 pi = 380.132711 cm^2
The central angle:
250/380 (2 Pi) = 4.13367454 radians
- PuzzlingLv 78 months 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
About 4.13 radians
- billrussell42Lv 78 months 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