Question

The central angle of an arc measures 75°. The diameter of the circle measures 6 meters. What is the area of the sector to the nearest tenth of a square meter?

Answer 1

The area of the sector is 5.89 m²

Explanation:

Given:

Central angle of the arc, α = 75°

Diameter of the circle, d = 6 m

Radius of the circle, r = 3m

Area of the sector, A = ?

We know:

$Area = \frac{\alpha }{360} X \pi r^2$

On substituting the value we get:

$Area = \frac{75}{360} X 3.14 X (3)^2\\\\A = 5.89 m^2$

Therefore, the area of the sector is 5.89 m²