Question

ments
nts
ns
Mai says, "I know how to find the area of a sector or the length of an arc for central angles like 180
degrees or 90 degrees. But I don't know how to do it for central angles that make up more complicated
fractions of the circle."
1. In the diagram, the sector's central angle measures 8 degrees and the circle's radius is r units. Use
the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and
radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded
sector, and the length of the arc defined by the sector.
160%
5 in

Answer 1

The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively

How to find a sector area, and arc length?

For a sector that has a central angle of θ, and a radius of r;

The sector area, and the arc length are:

$A = \frac{\theta}{360} * \pi r^2$ --- sector area

$L = \frac{\theta}{360} * 2\pi r$ ---- arc length

How to find the given sector area, and arc length?

Here, the given parameters are:

Central angle, θ = 160

Radius, r = 5 inches

The sector area is

$A = \frac{\theta}{360} * \pi r^2$

So, we have:

$A = \frac{160}{360} * \frac{22}{7} * 5^2$

Evaluate

A = 34.92

The arc length is:

$L = \frac{\theta}{360} * 2\pi r$

So, we have:

$L = \frac{160}{360} * 2 * \frac{22}{7} * 5$

L = 13.97

Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively

Read more about sector area and arc length at:

https://brainly.com/question/2005046

#SPJ1