What is the EXACT AREA of a ring that is 2 in wide and has an inside diameter of 1 and 1/4 inches?

Geometry word problem - how to find the exact area of a ring.
TabletClass Math Academy
Help with Middle and High School Math
Test Prep for High School Math, College Math, Teacher Certification Math and More!
All Courses - TCMathAcademy....
✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.
Popular Math Courses:
Math Foundations
tabletclass-ac...
Pre-Algebra
tabletclass-ac...
Algebra
tabletclass-ac...
Geometry
tabletclass-ac...
Algebra 2
tabletclass-ac...
Pre-Calculus
tabletclass-ac...

[@johnutting9615]

The question is a bit ambiguious as there is a ring 2in wide( width ?) With an inside diam of 1.25 in . Did anyone else have this interprtation?

[@tommybotts]

YES!!

[@barrieheald5823]

So did I

[@56edb]

He shows the big ring diameter as 2" and the small ring diameter as 1 1/4" . If that's true couldn't you just subtract the area of the small ring from the area of the large ring?

[@markjackson5806]

Yes, maybe the person writing these questions should read them three times.

[@walterdyer8753]

yes

[@SteveSearle]

"What is the EXACT area of the cross section of a pipe with an outside diameter of 2 inches and an inside diameter of 1.25 inches" is the correct description of the problem. 2 inches wide implies the wall thickness.

[@glennarmstrong7891]

The question would have been clearer had you said "outer diameter" (as you did with inner diameter)rather than two inch wide ring. I was looking at it like a two inch wide finger ring.

[@jaypetach5598]

Great episode. Originally, I was confused by the word “wide.” I didn’t associate that with the outside diameter. Instead, I thought of the 2” as the difference between the outside and inside diameters. Still, I love these episodes. I’m relearning all the math I’ve forgotten since college.

[@nyneeveanya8861]

Okay, got to your drawing and seen I had misinterpreted the question. I thought the ring was 2” wide along the whole circumference of the circle and the inner hole was 1 1/4” this would make the diameter 5 1/4” for the complete figure so find area of complete figure and subtract area of inner hole to get area of just the ring.

[@tassietiger5500]

Yes certainly a trick question. Where does it say "inside" area? It may be the outside areas or the area occupied by the ring itself?

[@paulbains9152]

If its a ring , the inside is empty , so you can put it on her fat finger .

[@davidjones-vx9ju]

what does 2 inches wide mean? diameter?

[@tommybotts]

The outside diameter.

[@terry_willis]

IMO the question is vague/ambiguous. I thought he was referring to a piece of a cylinder, such as a tube that was 1-1/4" in diameter, with a 2" slice, e.g. if you had a 1-1/4" diameter tube one foot long and you cut off a piece of that which was 2" wide (leaving a 10" tube). Then I thought the question asked for the area of the outside AND inside area of that tubular slice. The word ring threw me off - I first pictured a ring on your finger. The wording sounds like there is only one ring, not two. The question could have been "If you have 2 concentric circles, the larger 2" in diam and the smaller 1.25" in diameter, what is the area of the portion between the two circles?".

[@rustyknott-W.D]

I agree. I was told by a math teacher when I was in high school that I was a math "dummy". I believed her, avoiding math at all costs and got a liberal arts education. I used that to engage in a career in land surveying, becoming a registered professional land surveyor. The first part of that process is taking a national 8 hour "In Training" exam that is mostly advanced mathematics. Passed it on my first try. Once I started using math to solve real world problems, math became easy. This guy couldn't explain water to a fish.

[@Kleermaker1000]

Come on, US Americans, don not be stubborn and leave those inches, feet etc. behind you and embrace the metric system. It is so much easier for all of us.

[@barrieheald5823]

The drawing of the ring made the problem clear but the solution can be shortened considerably. The area of a circle is given by Pi x (diameter)squared divided by 4.If the outside diameter is D and the inside diameter is d, the required area is Pi x ((D) squared-(d)squared))/4. We now have the difference of two squares: (D)squared-(d)squared which can be written (D-d) x (D+d) i.e. ((8/4+5/4) x (8/4-5/4) giving the area as Pi x (39/64) square inches.

[@MrMousley]

So .. that's the area of a 2 inch diameter circle MINUS the area of a 1 1/4 inch diameter circle then. The diameters being 1 inch and 5/8 of an inch Pi x 1 squared - Pi x 5/8 squared ..... Pi x 1 - Pi x 25/64 64 - 25 = 39 Answer 39/64 x Pi Which, without a calculator handy, is my answer.

[@MathsMadeSimple101]

The wording of the question makes you question the wording of the question of the wording of the question of the wording of the question of the wording of the question.

[@kevinreist7718]

Exact? Pi isn't a rationale number so "Exact" is difficult to claim. How many decimal places are you considering to be "Exact"?

[@MrBloof]

Pi has infinite decimal places (we think) when represented in base 10. Even Though pi is irrational, the value can still be represented in the equation/answer and give complete accuracy due to the properties pi has in geometry . Increasing decimal places affects precision of your answer, but if you use the value of pi it will give you an exact answer. This is a similar concept to how e is used in Euler‘s equations.

[@kevinreist7718]

@@MrBloof Figures don't lie, but liars do figure.

[@MrBloof]

I have no idea what you mean by this lol. Did you understand the explanation?

[@li358690]

The outer ring radi = 1" Inside ring radi = 5/8" So the exact = 64/64 - 25/64 = 39/64 × 3.14 = 1.9135

[@babaji1947]

When I read RING, I assumed the ring to be cylindrical and not flat. I, therefore, assumed you were looking for the surface area of the circular cylinder. You should have clarified that in the question.

[@akash_mv]

When you say it's a ring it's presumed to be solid ring (even telling it as width is wrong) so if it's a ring (solid one) then it's diameter will be 0.75 inch (2 -1.25 inch) . Then you may have to calculate the average circumference of inner and outer diameter. ...and will be = 7.06 inch (3.142×2)+(3.242×1.25)/2 ..that will be average circumference. Which will be length of a rectangle Now you need to calculate the circumference of the solid ring which will be = 2.357 3.142×0.75. This will be considered as width of rectangle and length will be (average circumference )calculated previously. (This will be like a paper with is turned around the ring. ) here pai considered to be equal to 3.142. The result will be 16.64 square inch. 7.06×2.357 😊😊😊😂

[@peterfung4494]

why don't you use 22/7 instead of 3.14 ?

[@throngcleaver]

So, we're back to that racetrack issue again...

[@rustyknott-W.D]

Here we go again, again. Which area are we talking about? The inside area or the area encompassed by the outer edge of the ring? There are two possible solutions. Or are we talking about the area of the donut minus the hole? Be specific, for crying out loud. Typical word problem nonsense. The area of a circle is Pi times the radius squared, pure and simple. All you have to do is calculate the area of both circles and then subtract the lesser area from the larger area to get the area of the remaining donut. Quit making simple problems hard. Also, quit using inches or millimeters or whatever in your examples and use units instead. One circle has a diameter of 2 and the other has a diameter of 1.25, get it? It doesn't matter which system of measurement you use to arrive at the correct answer.

[@suemoore1965]

Amen... I agree ❤❤❤

[@russelllomando8460]

good one, thanks

[@polyphonicclix]

Could we have the question in metric please?

[@davidjones-vx9ju]

why?

[@kennethdias9988]

7.85 pi x diameter is circumference x width the ring is a small cylinder

[@jamesriley5057]

shoot. I thought he was talking about a torus, so I based my calc on that before I clicked the link. Oh well. thanks for the lesson!

[@user-ri6rn7ti5h]

2*1/1/4 = 2*1/4 = 2/4 (x+2x-4)

[@26Jorgeb]

We are talking of the cross sectional area here?

[@paulbains9152]

Area of Rsq = 5/8 sq =1.2453571 . 1 sq = 3.1428571 . therefore difference is 1.8975 sq inches .

[@tommybotts]

1) A = pi x r2 2) radius of ring is 1 inch 3) pi x 1" squared = 3.1416 in squared 4) Area = 3.1416" squared

[@davidjones-vx9ju]

minus the inside

[@tommybotts]

@@davidjones-vx9ju ???

[@davidjones-vx9ju]

the original post says..."2 inches wide" wide is not diameter @@tommybotts

[@tommybotts]

@@davidjones-vx9ju Yes it is! There's an outside and inside dia of a ring. The sentence does not specify which dia is to be used. My answer is correct - which is to say it is the EXACT AREA of a ring 2" wide.

[@davidjones-vx9ju]

merely your opinion ... a rectangle has width and length ,not a circle@@tommybottswhat language do you really speak?

[@silverhammer7779]

Technically, since Pi is an irrational number, no result that includes Pi as a multiplier can be exact. As usual, your wording of the problem is ambiguous. In the Real World, the area would be approximately 1.914 square inches since three decimal places is sufficient for most purposes.

[@rustyknott-W.D]

In my field, surveying, we usually go to 4 decimal places just to be anal but only measure to decimal places. We don't use inches, either. We use decimal feet or go metric, depending on the project, which is standard for engineering also. Only whores, carpenters and architects use inches for measurement.

[@silverhammer7779]

@@rustyknott-W.DI'm a retired engineer. I used to do most things to 4 places then round off to three. As a practical matter, trying to measure certain materials like aluminum alloy to four places is ridiculous because of aluminum's high alpha (coefficient of thermal expansion). European architects still measure everything in millimeters, IIRC. Maybe European whores and carpenters do, too 🤔😁

[@rustyknott-W.D]

Good one! I meant American civil engineering, whores, carpenters and architects, sorry. We surveyors usually measure to the 100th of a foot and only go to more decimal places when coping with extremely long distances. We also have to use the metric system as State Plane and UTM coordinates are metric. We also have to be conversant in pre-colonial and pre-metric systems of measurements, such as the Spanish and French "vara", leagues, etc. In the Public Land Survey system we use the chain, which is 66 feet and is divided by 100 links, each of which is 0.66 feet.Then there is the difference between the standard foot and the international foot, both of which are defined in terms of the meter, by the way. No wonder people say we can be grumpy. @@silverhammer7779

[@raynewport9395]

You probably meant annulus rather than ring.

[@dazartingstall6680]

In real units, 393.144375π mm^2

[@pamalogy]

A ring is not flat. It is round. So we need to multiply 39/64(pi) by pi. The correct answer is 39/64(pi^2).

[@EdSym1]

39/64pi

[@tesladan7873]

The answer is ambiguous. The answer is 1.9144 sq in. If you were purchasing something to cover an area, you would reply in decimal places. “I have 1.9144 square inches to paint”. You wouldn’t tell someone else “I need enough paint to cover 39/64” X pi surface area. People can deal with 1.9144 square inches. You don’t give answer with further math problems to solve. Your answer was NOT EXACT.

[@li358690]

1.2265

[@ab_ab_c]

You have some of the worst worded questions/problems. The problem should be: "What is the area between an outer circle & an inner circle, if the outer circle diameter is 2" and the inner circle diameter is 1 1/4"? Knowns: The formula for the area of a circle is: A = r² * π Problem Solution: Outer circle area - inner circle are = area between the circles. A1 - A2 = Area between the circles A1 = (2/2)² * π = 1² * π = π A2 = (1 1/4 / 2)² * π = (5/4/2)² * π = (5/8)² * π = 5² / 8² * π = 25/64 * π Area between the circles = π - 25/64 * π = π (1-25/64) = π (64/64 - 25/64) = π(39/64) = (39/64)π in²

[@lizardfirefighter110]

Know one is able to calculate the EXACT area because pi is not an EXACT number.

[@bobcornwell403]

An exact area would be: pi(1")² - pi(5/8")²

[@mahamunibalakrishnan8263]

11 sq.invhes.

[@elliotlambert3817]

Rings have diameters and what yo describe could be an anulus tell you kids.

[@rockitsurjon8629]

I have reported this channel since it may offend some Oregon and California students. They're not educated enough to know why so I am helping them out.

[@faisaltweit8445]

Too much talking, god help your students.

[@bluejedi723]

Why should i care?

[@tomtke7351]

if you were engineering inclined you'd be interested... suppose you need to construct a ring that's 100ft outter diameter with 75 ft diameter cutout... how much paint would you need to cover it if 1gallon covers 200 sq-ft?

[@bluejedi723]

and why would something like that need to built? as far as paint, your either gonna buy to much or not enough@@tomtke7351

[@paulbains9152]

@@tomtke7351 I am an engineer , and would have , asked , if the outer ring was made of round stock , what is the volume in cubic inches ? I got .4091031 cu in .

[@pibbles-a-plenty1105]

I don't buy it. My feeble mind says that there is no such thing as an "exact" area of a circle. The calculation is contaminated with an irrational number, pi. It reminds me of the cliche, "figures lie, liars figure." 🤨 Of course if you want real world precision just use a longer pi. 😊

[@tomtke7351]

trying to TRICK you. Anything dealing with pi that has to be exact requires the answer to be expressed in terms of pi. Why? I dunno! Or... because someone wants to make clear there's no number that's exactly = pi.😊

[@davidjones-vx9ju]

area is never expressed as/in pi

[@Kerbeygrip]

Inches inches inches and fractions of inches. Please join the real world of scientists and engineers worldwide and use the metre and centi/millimeters. I am 77 and have been educated from the age of 11 in SI units. How much longer for the world to have a single system? Well, YOU are not helping. I taught physics to A Level until I retired. Never an inch in sight. Went out in 1957 for goodness sake! My students went to top Universities. They would not have got in by miles (oops kilometers) but definitely not by inches......