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Etrujillo
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A sector in a circle is a region bounded by two radii and an arc of the circle. It is similar to a slice of pizza, with the radii acting as the crust and the arc as the toppings.
To find the area of a sector in a circle, you can use the formula A = (θ/360)πr², where θ is the central angle of the sector and r is the radius of the circle. This formula uses the fact that the area of a whole circle is πr², and the ratio of the central angle θ to the full angle of 360 degrees is the fraction of the circle's area that the sector covers.
The value of π used in finding the area of a sector is the same as the value used for finding the area of a circle, which is approximately 3.14159. It is a constant value that represents the ratio of a circle's circumference to its diameter.
Yes, the area of a sector can be expressed in terms of π. In fact, the formula for finding the area of a sector (A = (θ/360)πr²) already includes π. This means that you can leave the answer in terms of π without having to calculate its decimal approximation.
No, the area of a sector cannot be negative. It is always a positive value, as it represents the amount of space covered by the sector within the circle. If the calculated area is negative, it means that there was an error in the calculations or that the central angle was incorrectly measured.