How do you find the measure of a central angle in degrees? The only information i have is circumference, area, diameter and radius of the circle.

Question

anonymous · Answer

By area, do you mean the area of a sector of the circle? or the total area?

anonymous · Answer

the total area

anonymous · Answer

Hmm, that won't do. It doesn't look like you have any info you need to find the central angle.
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You need to know something about the particular sector. The diameter is just twice the radius. The circumference and area of the circle only tell you about the whole circle, not the sector.

By any chance, are you given a ratio of the circumference to the sector's arc length, or total area to sector area? That would be a step in the right direction.

anonymous · Answer

Well i am supposed to be finding a bunch of information on a ferris wheel (the singapore flyer).  It asks me a bunch of questions in a row. Hold on ill post the questions.

anonymous · Answer

Complete the following tasks and calculations. You must show all work and steps to receive full credit.

        Name of the ferris wheel
        Diameter of the wheel (in meters)
        Number of cars or compartments
        Circumference of the wheel (in meters)
        Area of the wheel (in meters)
        Measure of a central angle in degrees
        Measure of a central angle in radians
        Arc length between two cars or compartments
        Area of a sector between two cars or compartments

anonymous · Answer

Okay, so there's some hidden info here. The compartments on a Ferris wheel have to be spaced evenly apart, right? How many compartments are there?

anonymous · Answer

28 compartments

anonymous · Answer

Are you there?

anonymous · Answer

28's a bit much to draw, so I'll just stick to 10 as an example:
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Let's pretend the drawing is perfect, and that the circle can be cut into 10 equal-sized slices.

This means that the central angle (the angle between adjacent cars) is $\dfrac{360^\circ}{10}=36^\circ$, since there are 10 cars and thus 10 slices to the circle.

Let $r$ be the radius, then the circumference is $2\pi r$. The arc length $x$ of one of the 10 slices is given by the ratio
$$\frac{2\pi r}{360^\circ}=\frac{x}{\frac{360^\circ}{10}}=\frac{x}{36^\circ}$$