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

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2018

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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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