Final answer:
The area of the sector intercepted by a central angle θ = π/5 for a circle with a radius of 19.4 cm is calculated using the formula A = θ/2π × πr², which results in 118.752 cm². After rounding to maintain significant figures, the area of the sector is 120 cm².
Step-by-step explanation:
The area, A, of a sector intercepted by a central angle θ equals π/5 for a circle with radius r = 19.4 cm can be found using the formula:
A = θ/2π × πr²
First, we find the area of the whole circle using A = πr². With r = 19.4 cm, the area of the full circle is:
A = π × (19.4 cm)²
Then, since the sector is a fraction of the whole circle based on the angle θ, we calculate the proportion of the circle that the sector occupies. The area of the sector is thus:
A = (π/5)/2π × π × (19.4 cm)²
A = 1/10 × π × (19.4 cm)²
After doing the calculation:
A = 1/10 × 3.1415927 × 376.36 cm²
A = 118.752 cm²
To maintain proper significant figures, we should round our answer to two significant figures, because the radius was given to two significant figures. Therefore, the rounded area of the sector is:
A = 120 cm²