Area of a Segment

Find the area of the segment of a circle whose radius is 2 feet, formed by a central angle 70 degrees.

MY WORK:

Subtract area of triangle from area of the sector to obtain the area of the segment.

A = 70 degrees/2 times 4^2

A = 140

Area of triangle = 1/2 times 2(8) times 70 degrees

A = 8

140 - 8 = 132.

The book's answer is: 19.81.

What am I doing wrong?

greatwhiteshark said:

Find the area of the segment of a circle whose radius is 2 feet, formed by a central angle 70 degrees.

Click to expand...

Looks like you wandered off a bit, right off.

Area of circle

pi*r² = pi*(2 ft)² = 4*pi*ft² = 12.56637 ft² -- This sort of casts doubt on the book's answer.

Area of Segment

(4*pi ft²)*(70º/360º) = 2.44346 ft²

Where does that leave us?

Hello, greatwhiteshark!

Find the area of the segment of a circle whose radius is 2 feet, formed by a central angle 70 degrees.
The book's answer is: 19.81.

Click to expand...

tkhunny is absolutely correct.
The area of the whole circle is only: . 4(pi) .≈ .12.566 ft²
. . . So the book is way way off.


The area of the sector can be found by a proportion:

. . . Sector . . . . .70^o
. . . -------- . = . ------
. . . .Circle . . . . 360^o

. . . So: . Sector .= .(4pi)(7/36) .= .7pi/9 .≈ .2.443


The area of the triangle can be found with this formula:
. . . Area . = . (1/2) x (side) x (another side) x (sine of included angle)

So we have: . Triangle .= .(1/2)(2)(2)(sin 70^o) .≈ .1.879


Therefore: . Segement .= .Sector - Triangle .= .2.443 - 1.879 .= .0.564 ft²

On the other hand, maybe the book MEANT:
--- Radius = 4
--- Central Angle = 141.9º
:roll:
Books are no more reliable than the people who write, check, edit, review, and publish them.

tkhunny said:

On the other hand, maybe the book MEANT:
--- Radius = 4
--- Central Angle = 141.9º

Click to expand...

Of course . . . a perfectly understandable typo!

okay

There are similar questions like this in my pre-calculus math book. I will practice some more today and take it from there.