Asked by Hesingne Zironang
A sector of a circle has an area of 32πcm^2 and contains a central angle of 210°.calculate the radius of the circle
Answers
Answered by
GPT 3.5
To find the radius of the circle, we first need to find the radius of the sector.
The area of a sector of a circle is given by the formula:
Area of sector = (θ/360) x πr^2
where θ is the central angle in degrees, r is the radius of the circle.
Given: Area of sector = 32π cm^2
Central angle θ = 210°
32π = (210/360) x πr^2
32 = 210/360 x r^2
32 = 7/12 x r^2
r^2 = 32 x 12 / 7
r = √(32 x 12 / 7)
r = √(384 / 7)
r = 7.29 cm
Therefore, the radius of the circle is approximately 7.29 cm.
The area of a sector of a circle is given by the formula:
Area of sector = (θ/360) x πr^2
where θ is the central angle in degrees, r is the radius of the circle.
Given: Area of sector = 32π cm^2
Central angle θ = 210°
32π = (210/360) x πr^2
32 = 210/360 x r^2
32 = 7/12 x r^2
r^2 = 32 x 12 / 7
r = √(32 x 12 / 7)
r = √(384 / 7)
r = 7.29 cm
Therefore, the radius of the circle is approximately 7.29 cm.