Question

Find the area of a sector with a central angle of 140° and a diameter of 9.5 cm. Round to the nearest tenth.

2.9 cm^2
7.4 cm^2
110.3 cm^2
27.6 cm^2

Answer 1

27.6 cm²

Explanation:

The area of a sector is given by ...

A = (1/2)r²θ

where r represents the radius, and θ represents the central angle in radians.

The radius is half the diameter, so is 4.75 cm. The angle in radians is ...

(140°)(π/180°) = 7π/9

So, the sector area is ...

A = (1/2)(4.75 cm)²(7π/9) ≈ 8.77π cm² ≈ 27.6 cm²

The area of the sector is about 27.6 cm².