   Chapter 8.CR, Problem 32CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# The arc of a sector measures 40 ∘ . Find the exact length of the arc and the exact area of the sector if the radius measures 3 5  cm .

To determine

To find:

The exact length of the arc and the exact area of the sector.

Explanation

Formula:

Area of sector = Area of circle × (arc lengthcircumference)

Calculation:

The length of the arc = l

If x is the angle at the center obtained by the arc then the length of the arc is

l=x360×2πr=40360×2π(35)=19×2π(35)

=6π59=2π53

So, the length of the arc = 2π53 cm

To find the exact area of the sector:

Total circumference =2πr=2π(35)=6π5

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