What is the area of a sector with a central angle of 160 degrees and a diameter of 5.8m?

Solution:

Given central angle of a circle is 160 degrees

Diameter of circle is 5.8cm

We know that radius is half of diameter, r= d/2 = 5.8/2 = 2.9cm

A sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them.

We have formula for finding the area of a sector of a circle is given by

Area = 1/2 × r²θ, where, θ is the angle subtended at the center, in radians, and r is the radius of the circle.

Area = 1/2 × (2.9)(2.9)(160°)

Area = 1/2 × 1345.6

Area = 672.8 sq.m

The area of a sector of given circle is 672.8 sq.m

What is the area of a sector with a central angle of 160 degrees and a diameter of 5.8m?

Summary:

The area of a sector with a central angle of 160 degrees and a diameter of 5.8m is 672.8 sq.m