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?

To find the area of a sector of a circle when the radius (r) and arc length (s) are known, one can use the direct formula Area = (1/2) × r × s. In this problem, the radius is given as 10 cm and the arc length is 15 cm. Substituting these values into the formula yields Area = (1/2) × 10 cm × 15 cm, which equals 75 cm². Alternatively, one can first find the central angle (θ) in radians using the formula s = rθ, which gives θ = 15/10 = 1.5 radians. Then, applying the sector area formula A = (1/2)r²θ results in A = (1/2) × (10)² × 1.5 = 0.5 × 100 × 1.5 = 75 cm². Both methods consistently lead to 75 cm², matching option 3.