Final answer:
The area of a sector with a central angle of 4π/5 radians and a radius of 11 cm is 48.4π cm², which can be simplified and rounded to 152 cm² to match the significant figures of the radius.
Step-by-step explanation:
The task is to calculate the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm. To find the area of a sector, you would use the formula A = (1/2) • r² • θ, where A is the area of the sector, r is the radius of the circle, and θ is the central angle in radians.
Starting with the formula, substitute the given values:
A = (1/2) • (11 cm) ² • (4π/5)
Next, calculate the square of the radius:
A = (1/2) • (121 cm²) • (4π/5)
Then, multiply the terms:
A = (121/2) • (4π/5) cm²
After performing the multiplication:
A = (121 • 4π/(2 • 5)) cm²
A = (484π/10) cm²
Finally, divide 484 by 10 and multiply by π:
A = 48.4π cm²
However, since π is approximately 3.14159, multiplying 48.4 by π gives us:
A = 48.4 • 3.14159 cm²
This can be rounded to match the significant figures of the radius, which has two significant figures, giving us a final answer:
A = 152 cm², rounded to three significant figures.