This is my final math question of the night,please help me and show work!?

Question

A circle has a circumference of 100 yards. Find its area.
Use 3.14 inplace of pi.

Please show work to find the area.
The answer i got was 795.8 but in the back of the book they had got 796.2. I want to know how to do this so i can understand it on a test.
Thank-you for your time!

Answer 1

C = 100 yards
C = 2 pi r
100 = 2 pi r
50 = pi r
r = 50/3.14 (leave it since it is a long decimal)

A = pi x r^2
A = 3.14 x (50/3.14)^2
If you type this into a calculator you will get the answer the book got. If you round too early you will get your answer.

Answer 2

The circumference of a circle of radius r is C=2πr
The area of a circle of radius r is A=πr².
Use the first equation to find the radius of the circle, then plug that into the 2'nd equation to get the area.
If yui got 795.8 and the book says 796.2 you probably did it right and the book just used different numbers of significant digits in the computation.

Doug

Answer 3

You did the correct work, and got the same answer that I got. You and I both rounded the radius to the nearest hundredth. I redid the problem rounding the radius to different place values, and apparently the book rounded to the nearest thousandth. I don't have the original question, so I don't know what the book told you to round to. Basically, on your test, if they don't write what place value to round to, ask your teacher what place value to round to. Hope this helps!

Answer 4

radius = 100 / (2 * 3.14)
Area = Radius^2*3.14

I would guess that the difference between your answers is due to a rounding error since your answer is so close to the correct answer

Answer 5

C = 100 = 2 * pi * r
r = 100 / 2 / pi
r = 50 / pi

A = pi * r^2
= pi * 50^2 / pi^2
= 50^2 / pi
= 796.1783439