Find the area of a sector, given a central angle of 240degrees and a radius of 15 cm. Round your answer to the nearest tenth.
To find the area of a sector, you need to use the formula:
Area of a sector = (θ/360) * π * r^2
where:
- θ is the central angle in degrees
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the sector
Given the values in the question, we can substitute them into the formula:
θ = 240 degrees
π = 3.14159
r = 15 cm
Area of the sector = (240/360) * 3.14159 * (15)^2
Simplify the fraction:
Area of the sector = (2/3) * 3.14159 * 225
Calculate the values:
Area of the sector ≈ 471.238898
Rounding it to the nearest tenth, the area of the sector is approximately 471.2 square cm.