Final answer:
The correct answer is option b. 33. To find the area of a sector with a radius of 5 cm and a central angle of 150°, you apply the formula A = πr²×(θ/360), which gives a result of approximately 32.72 cm², rounded to 33 cm².
Step-by-step explanation:
The correct answer is option b. 33. To find the area of a sector, you use the formula A = πr² × (θ/360), where A is the area of the sector, r is the radius of the circle, and θ is the central angle in degrees.
To find the area of the sector, we can use the formula:
Area of sector = (central angle / 360 degrees) × πr²
Given that the radius is 5 cm and the central angle is 150 degrees, we can substitute these values into the formula:
Area of sector = (150 / 360) × 3.14159 × 5²
Calculating this expression, we find that the area of the sector is approximately 33 square centimeters, which matches with option b). In this case, with a radius of 5 cm and an angle of 150°, we calculate the area as follows:
A = π × (5 cm)² × (150°/360°)
A = π × 25 cm² × (5/12)
A = (π × 25 cm² × 0.4167)
A ≈ 32.72 cm²
So, rounding to the nearest square centimeter, the area of the sector is approximately 33 cm².