Which one of the following is the area of a sector of a circle of radi

Which one of the following is the area of a sector of a circle of radius 10 cm formed by an arc length of 15 cm?

10π cm²
15π cm²
75 cm²
150 cm²
This question was previously asked in
UPSC CAPF – 2018
The area of the sector is 75 cm².
The area of a sector of a circle can be calculated using the formula:
Area = (1/2) * r * L
where ‘r’ is the radius of the circle and ‘L’ is the length of the arc that forms the sector.
Given:
Radius (r) = 10 cm
Arc length (L) = 15 cm
Area = (1/2) * 10 cm * 15 cm
Area = 5 cm * 15 cm
Area = 75 cm²
Alternatively, the area of a sector can be calculated using the formula Area = (θ/360°) * πr², where θ is the central angle in degrees. To use this formula, one would first need to find the angle θ using the relationship L = rθ (where θ is in radians), or L = (θ/360°) * 2πr (where θ is in degrees). Using L = rθ, 15 cm = 10 cm * θ, so θ = 1.5 radians. Then, Area = (1/2) * r² * θ = (1/2) * (10 cm)² * 1.5 radians = (1/2) * 100 * 1.5 cm² = 50 * 1.5 cm² = 75 cm². Both methods yield the same result.
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