How do I find the area of a doughnut when I only know the outside measurements?

Question

I'm figuring how much carpet I will need to recarpet an outer hallway around the outside of a building. I have a measurement of 240 approxiamately for the outside and it measures 205 around the inside wall, and its only 6 feet wide. I'm goin braindead here.......Help!

Answer 1

A doughnut is a torus. You don't have one. You need to calculate the area of the outside circle and the area of the inside circle and subtract the two. The easiest way it to take the average of the outside and the inside wall and multiply by 6.

Answer 2

If it is a circle, then to determine the area use P r squared. You will need the radius of the circle, not the circumference. Then determine the total area of the outer circle (the buidling) then determine the radius of the inner circle (it will be exactly 6 feet less than the outer circle) Do the math, and then subtract the area of the inner circle from the outer circle. You will be left with the total area of the hallway.
If the hallway is not a circle, then you can determine the actual area for each section, (length x 6) and add them up.
Remember, carper is lineal, meaning it does not turn in circles. If you truly have a circle, then you will need much more carpet than the area.

Answer 3

From the way you describe it I assume that the pathway for the carpet is circular. Therefore the area is calculated as follows:

A = Pi/4*(Do squared - Di squared) where Do is the outside diameter and Di is the inside diameter. And Pi is 3.1416 approximately.

Alternatively, if the measurements given are the outside and inside circumferences, find the average circumference and multiply by 6. The answer then is 1335 square feet or 148.3 sq yds.

Answer 4

If you have a circluar donut this is what you need to do assuming the measurements are the perimeter (circumference) of the circlular walls.

What you need to do is use the forumla for circumference to figure out the radius of each circle. Once you find the radius of each circle you can then find the area of both and take the difference to figure out how much carpet you need.

Innner wall
C=2(pi)r
205=2(pi)r
r=(205/(pir)
r=32.64ft

outer wall
C=2(pi)r
240=2(pi)r
r=(240/(pir)
r=38.197ft

Which gives us a width of about 6 feet like you said

Then the area of each

Outer Wall
A=(pi)r^2
A=(pi)(38.197)^2
A=4583.62 square feet

Inner circle
A=(pi)r^2
A=(pi)(32.64)^2
A=3346.96 square feet

Then take the difference

4583.62 - 3346.96 = 1236.66 square feet of carpet. I would probably buy a more beacue carpet won't turn corners so you will be doing alot of cutting

Answer 5

I'm not sure I understand when you say 240 for the outside - is that perimeter?

Also, are we talking rectangles or circles?

Nevertheless, here is what I would do: Calculate the area of the outside, disregarding the inside. Calculate the area of the inside. Subtract the second from the first.