Find the area of a sector, given a central angle of 240° and a radius of 15 cm. Round your answer to the nearest tenth please.
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To find the area of a sector, you need to know two things: the central angle of the sector (in degrees) and the radius of the sector.
The formula to find the area of a sector is given by:
Area = (θ/360) * π * r^2
Where:
- θ is the central angle of the sector in degrees,
- π (pi) is a mathematical constant approximately equal to 3.14159, and
- r is the radius of the sector.
In this case, the central angle (θ) is 240° and the radius (r) is 15 cm.
Substituting these values into the formula, we have:
Area = (240/360) * π * 15^2
Now, let's calculate it step by step:
Step 1: Simplify the fraction
240/360 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 120.
240/360 = 2/3
Step 2: Substitute the values into the formula
Area = (2/3) * π * 15^2
Step 3: Calculate the area
Using a calculator, evaluate the expression:
Area ≈ (2/3) * 3.14159 * 15^2 ≈ 471.23889803846896
Rounding this answer to the nearest tenth, we get:
Area ≈ 471.2 square cm
Therefore, the area of the sector is approximately 471.2 square centimeters.