Area of a Segment?.

I

iosman123

New member
Joined
Jul 25, 2019
Messages
12
Hello,


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?

thanks
iosman
 
iosman123 said:
Hello,


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?

thanks
iosman
Click to expand...
"The book's answer is: 19.81."

There is something wrong with your answer and that answer!

The area of the Total circle = pi * r2 = 3.141593 * 22 ~ 12 sq.ft

How can the segment be anything more than that?
 
What formulas are you using for the area of the sector, and for the base and height of the triangle? I would expect to use radians in the former, and a trig function in the latter. I also can't see how your calculations would yield the numbers you got, so maybe you didn't really do what you said you did.

Show us your formulas and your reasoning, so we can talk about where it is wrong.
 
Your work is kinda hard for me to decipher, and I'm also a little confused at your terminology. You're looking for the area of the "segment" which I at first interpreted in this instance as being a synonym of "sector." However, you mention subtracting the area of a triangle (which triangle? where?) from the area of the sector to obtain the area of the segment. Are you perhaps trying to find the arc length? Of course it then wouldn't make sense for that to be expressed as an area, so....
 
A segment of a circle is, as the OP stated, a sector minus a triangle. The only issue is that both areas were incorrect. The link includes appropriate formulas; note that if angles are in degrees, there should be a 360 and a sine function involved.

But also, as SK pointed out, the book's answer is wrong; even the square containing the entire circle is 16 square feet, less than they claim for the segment (assuming it is the answer for the right problem).
 
Hmm. You learn something new everyday. I'd never heard of the segment of a circle before.
 
iosman123 said:
Hello,


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?
0x8007045

thanks
iosman
Click to expand...


thanks my issue has been fixed.
 
Out of curiosity (and perhaps to help others), how was it fixed? Was it determined that the book's answer was indeed wrong, or that you were looking at the wrong answer, or ... ?

And I assume you used the right formulas and got an actually correct answer; others might like to see that work.
 
Dr.Peterson said:
Out of curiosity (and perhaps to help others), how was it fixed? Was it determined that the book's answer was indeed wrong, or that you were looking at the wrong answer, or ... ?

And I assume you used the right formulas and got an actually correct answer; others might like to see that work.
Click to expand...
Mr. IosMan has a habit of fixing issues (possibly from other websites) without showing work. For example:

https://www.freemathhelp.com/forum/...x-sec-x-sec-x-cot-x-csc-x.117446/#post-463696
 
You must log in or register to reply here.
Top