A tan is shaped as a sector of a circle radius 12cm with the angle 110 at the centre calculate the area of the fan
Mathematics · High School · Thu Feb 04 2021
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To calculate the area of a sector of a circle (which is the shape of the fan you've described), you can use the formula for the area of a sector:
Area of a sector = (θ/360) × π × r²
Where: - θ is the central angle of the sector in degrees. - π is Pi, a mathematical constant approximately equal to 3.14159. - r is the radius of the circle.
Given: θ = 110 degrees r = 12 cm
Now, let's plug in the given values into the formula:
Area of sector = (110/360) × π × (12²)
First, compute 12²: 12² = 144 cm²
And then multiply by π and 110/360:
Area of sector = (110/360) × π × 144 ≈ 0.3056 × π × 144 ≈ 44.03 × π ≈ 44.03 × 3.14159 ≈ 138.23 cm² (rounded to two decimal places)
So, the area of the sector (fan) is approximately 138.23 square centimeters.