Final answer:
The area of the sector with an arc length of 4π and a radius of 9 cm is 57 cm², after applying the sector area formula and rounding to two significant figures.
Step-by-step explanation:
To find the area of a sector given the arc length and the radius, we use the formula:
A = (L × r) / 2
Where 'A' is the area of the sector, 'L' is the arc length, and 'r' is the radius of the circle.
Here, the arc length L = 4π cm and the radius r = 9 cm.
Now, let's plug these values into the formula:
A = (4π × 9 cm) / 2
A = (36π cm²) / 2
A = 18π cm²
Since π is approximately 3.14159, we can calculate the numerical value as:
A = 18 × 3.14159 cm²
A = 56.54867 cm²
However, since our given measurements have only one or two significant figures, the area should be reported in two significant figures:
A = 57 cm²