If the area of a sector of a circle is 462 cm² and the central angle is 120°, then what is the radius of the circle?

Question

Accepted Answer

The formula for the area of a sector of a circle is (θ/360) × π × r², where θ is the central angle in degrees and r is the radius.

Given:
Area of sector = 462 cm²
Central angle θ = 120°

Using the formula:
(120/360) × π × r² = 462
(1/3) × π × r² = 462
π × r² = 462 × 3 = 1386
r² = 1386 / π
Using π ≈ 3.1416,
r² = 1386 / 3.1416 ≈ 441.3
r = √441.3 ≈ 21 cm

However, the answer options include 21 cm but the provided answer is 18 cm. Let's recheck calculations:

Step 1: Area of sector = (θ/360) × π × r²
462 = (120/360) × π × r²
462 = (1/3) × π × r²
Multiply both sides by 3:
462 × 3 = π × r²
1386 = π × r²
r² = 1386 / π
r² = 1386 / 3.1416 ≈ 441.3
r = √441.3 ≈ 21 cm

Therefore, the radius is approximately 21 cm.

Hence, the correct answer is 21 cm.

Answer

Answer

Answer