Final answer:
To find the area of a circle from the given circumference, divide the circumference by π to find the radius, then use the formula A = πr², ensuring that the result has the same number of significant figures as the radius.
Step-by-step explanation:
The student is asking how to find the area of a circle given that π times the radius (πr) is 9.42 cm. To find the area of a circle, the formula A = πr² is used, where A represents the area, π is Pi (approximately 3.14159), and r is the radius. First, the radius must be found by dividing the circumference (9.42 cm) by π (9.42 cm ÷ π). Then, square the radius and multiply by π to get the area. In practice with significant digits, it would look like this:
A = πr² = (3.1415927...) × (1.2 m)² = 4.5238934 m²
However, since the radius has only two significant figures, the area would be limited to two significant figures as well:
A=4.5 m²