The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle.

Answer Details

To solve this problem, we need to use the formula for the area of a sector of a circle, which is: Area of sector = (θ/2) × r² where θ is the central angle subtended by the sector, r is the radius of the circle, and the angle is measured in radians. In this problem, we are given the area of the sector and the central angle, so we can plug in these values and solve for the radius: 3 = (1.5/2) × r² Multiplying both sides by 2/1.5, we get: 4 = r² Taking the square root of both sides, we get: r = 2 Therefore, the radius of the circle is 2 cm. We can check our answer by plugging it back into the formula for the area of the sector: Area of sector = (1.5/2) × 2² = 1.5 × 2 = 3 This confirms that our answer is correct.