Question

Find the area of the smallest sector. Central angle: 140 degrees, Radius: 8m. Round to the nearest hundredth.

a) 123.17 m²
b) 154.66 m²
c) 176.71 m²
d) 193.22 m²

Answer 1

The area of the smallest sector is approximately 289.01 m².

Step-by-step explanation:

The area of a sector is given by the formula A = (θ/360) * π * r², where θ is the central angle and r is the radius.

Given that the central angle is 140 degrees and the radius is 8m, we can substitute these values into the formula as follows:

A = (140/360) * π * (8m)² = (7/18) * π * 64m² = 4.5238934 * 64m² = 289.0053376m²

Rounding to the nearest hundredth, the area of the smallest sector is approximately 289.01 m² (option A).