Final answer:
To find the area of the circle from the sector's area and arc measure, set up a proportion involving the sector's area formula and solve for the radius squared. Using the radius, calculate the circle's area with A = πr² and round to the nearest tenth.
Step-by-step explanation:
The question involves finding the area of a circle given the area of a sector and its arc measure. Since the sector's area is proportional to the arc measure and a full circle has 360 degrees, we can set up a proportion to find the area of the entire circle. Using the formula for the area of a sector, which is Area of sector = πr² * (arc measure/360), we can solve for r².
To find the circle's area using the given sector's area of 873 square millimeters and an arc measure of 63 degrees, we use the formula:
πr² = (Area of sector * 360) / (arc measure)
πr² = (873 mm² * 360) / 63
After calculating, we find the radius squared, and then apply the formula A = πr² to find the total area of the circle, making sure to round to the nearest tenth as required.