Find the area of a sector of a circle with radius 6 cm if the angle of the sector is 60 degrees. (Use π≈3.14)
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Step-by-Step Solution
Step 1: Identify Given Values
We are given the radius of the circle, r, as 6 cm, and the angle of the sector, θ, as 60 degrees. We also need to use the approximation π≈3.14.
Step 2: Formula for Area of a Sector
To find the area of a sector, we use the formula that relates the central angle of the sector to the total angle of a circle (360∘).
Step 3: Substitute Values into Formula
Now we substitute the given values of θ=60∘, π=3.14, and r=6 cm into the formula for the area of a sector. This sets up the calculation.
Step 4: Simplify the Fraction
First, we simplify the fraction 360∘60∘, which reduces to 61. This makes the subsequent calculations easier.
Step 5: Calculate the Square of the Radius
Next, we calculate the square of the radius, 62, which is 36 cm2.
Step 6: Perform Multiplication
Now, we multiply 61 by 36 cm2, which simplifies to 6 cm2. The expression becomes 6 multiplied by 3.14.
Step 7: Final Calculation
Finally, we perform the last multiplication: 6×3.14=18.84. This gives us the area of the sector in square centimeters.