In many real-world scenarios, we encounter partial circles, such as pizza or pie slices. To measure the circumference and area of these parts, we must first determine the fraction of the whole circle they represent. We can find this fraction by dividing the angle of the arc by the total angle of the circle, which is 360 degrees.
To compute the circumference of a partial circle, we need to multiply the fraction of the circle it represents by the full circumference formula. This results in the formula for the circumference of a partial circle: C = (2πr) × (θ/360), where C is the circumference of the partial circle, r is the radius of the circle, and θ is the angle of the arc in degrees.
Similarly, to calculate the area of a partial circle, we need to multiply the fraction of the circle it represents by the full area formula. This gives us the formula for the area of a partial circle: A = (πr²) × (θ/360), where A is the area of the partial circle, r is the radius of the circle, and θ is the angle of the arc in degrees.
For example, if we have a pizza with a radius of 10 inches and a slice that covers an angle of 45 degrees, we can use these formulas to find the circumference and area of the slice. Therefore, by using the fraction of the circle that a partial circle covers and modifying the formulas accordingly, we can determine the measurements of a partial circle.