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Old 11-09-11, 08:49 PM Thread Starter   #1
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Give me a hand on this Tech Math


It's home work for college and so far this is the only question I've gotten stuck on.

"Sheet metal is used to construct a trough whose ends are isosceles trapezoids. How many square feet of sheet metal is used to form the trough? How many gallons of water will the trough hold? Note 231 in^3 = 1 Gallon

IMAG0003.jpg

So far I've come up with Surface Area of 131.33 ft sqrd with 1,043.69 Gallons. I got my answer by taking the area of the bottom, sides, and front and back but not the top since the trough has no top. The volume well that was self explanatory. I'm just looking for some other thoughts on this to compare my answer to.

EDIT: Forgot to mention I DID convert the 12ft to 144in.

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Last edited by Ronbert; 11-09-11 at 08:58 PM.
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Old 11-09-11, 09:22 PM   #2
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I just did the SA and came up with 135.3. First, everything I'll do will be inches.

The bottom is clearly 60x144, which is 8640.
One of the long side is 144 x the hypotenuse. You know that y=24, and x is half the distance between 80 and 60, so it's 10. So square both of those and add them and you get 676, then take the square root and you get 26. So 144x26 = 3744. You've got two of those sides so the long sides total 7488.
The front is made of up a couple of parts, one is the square and then basically the two triangles. Since they're both the same size triangles you can thing of them as just 1 rectangle. So the square is 60x24, which is 1440. The remainder is 2 triangles of 10 x 24, or just one rectangle of 10x24, which is 240. The overall size of the front then is 1680. The back is the same size, so the front and back is 3360.

Bottom, sides and front/back is: 8640 + 7488 + 3360 = 19488 sq inches. To get square feet, divide by 144 (12 inch by 12 inch), and you get 135.3 (repeating).

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Old 11-09-11, 09:52 PM Thread Starter   #3
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Hmm... I guess I didn't think of that height being slant height instead of actual height. I'll have to re-work this.

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Old 11-10-11, 09:08 AM   #4
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Quote:
Originally Posted by Quigsby View Post
The front is made of up a couple of parts, one is the square and then basically the two triangles. Since they're both the same size triangles you can thing of them as just 1 rectangle. So the square is 60x24, which is 1440. The remainder is 2 triangles of 10 x 24, or just one rectangle of 10x24, which is 240. The overall size of the front then is 1680. The back is the same size, so the front and back is 3360.
Correct, but there's an easier way: the area of a trapezoid is (b1+b2)/2 * h, where b1 and b2 are the parallel bases and h is the height. In this case, that would be (60+80)/2 * 24 = 1680.

The rest of the math checks out.

Here's another practice question, Ronbert: Change that 24in height to x. Now how many inches does the height need to be to make the trough hold 1500 gallons exactly? Or, given 100 ft^2 of sheet metal, design a trough to hold the maximum amount of water possible, given the constraint that the area of the base has to be 8200 in^2.

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Old 11-10-11, 09:59 AM   #5
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Originally Posted by LoneWolf121188 View Post
Change that 24in height to x. Now how many inches does the height need to be to make the trough hold 1500 gallons exactly? Or, given 100 ft^2 of sheet metal, design a trough to hold the maximum amount of water possible, given the constraint that the area of the base has to be 8200 in^2.
God. You Americans and your stupid units. The fact that you guys don't adopt the metric system, plus your silly nonsensical letter-sized paper makes me so angry, sometimes. The fact I have to convert the weather to Celsius each day by subtracting 32 and multiplying by nine-fifths is enough to make me want to scream.

If I grew up in the US, I would probably flunk out of school, for the simple reason that I'd never hand in an assignment or test due to my strict adherence to religious beliefs [my beliefs being that you should use a system of units and aspect ratio of paper which actually makes mathematical sense].

Yes, I too wonder why I bother getting up in the mornings.

Last edited by Mother Goose; 11-10-11 at 10:07 AM.
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Old 11-10-11, 10:11 AM   #6
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Quote:
Originally Posted by Mother Goose View Post
God. You Americans and your stupid units. The fact that you guys don't adopt the metric system, plus your silly nonsensical letter-sized paper makes me so angry, sometimes. If I grew up in the US, I would probably flunk out of school, for the simple reason that I'd never hand in an assignment or test due to my strict adherence to religious beliefs [my beliefs being that you should use a system of units and aspect ratio of paper which actually makes mathematical sense].

It's a wonder I get up in the mornings.
Well we have the older units. Could you imagine converting all those old family recipes? I mean the tsp. is easy but quarts and liters and cups and pints. Why dont you come to my house and rewrite all on my cook books. Also what do I do with my standard tools? The threads pitch and bolt diameter on machine screws alone would play hell as well

We will remain backward thank you much.

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Old 11-10-11, 10:18 AM   #7
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Quote:
Originally Posted by Archer0915 View Post
Well we have the older units. Could you imagine converting all those old family recipes? I mean the tsp. is easy but quarts and liters and cups and pints. Why dont you come to my house and rewrite all on my cook books. Also what do I do with my standard tools? The threads pitch and bolt diameter on machine screws alone would play hell as well

We will remain backward thank you much.
There is a movement every now and again to go Metric. Maybe it will happen some day, who knows?

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Old 11-10-11, 10:22 AM   #8
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Originally Posted by Quigsby View Post
There is a movement every now and again to go Metric. Maybe it will happen some day, who knows?
Honestly the only real advantage to keeping both in my opinion is machine screws. I have found no metric comprable to the 3/8 16.

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Old 11-10-11, 12:45 PM   #9
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Quote:
Originally Posted by Mother Goose View Post
God. You Americans and your stupid units. The fact that you guys don't adopt the metric system, plus your silly nonsensical letter-sized paper makes me so angry, sometimes. The fact I have to convert the weather to Celsius each day by subtracting 32 and multiplying by nine-fifths is enough to make me want to scream.

If I grew up in the US, I would probably flunk out of school, for the simple reason that I'd never hand in an assignment or test due to my strict adherence to religious beliefs [my beliefs being that you should use a system of units and aspect ratio of paper which actually makes mathematical sense].

Yes, I too wonder why I bother getting up in the mornings.
Seriously. As an aerospace engineer, I about wanted to shoot myself when I discovered that Boeing, Lockheed, and even NASA still use imperial units. SpaceX is the only US aerospace company I know of that uses metric. Ridiculous.

My grade in my Flight Dynamics class is actually a few points lower than it should be because the definition of the pound is completely stupid and nonsensical.

Mother Goose, you'll be happy to hear that most higher level STEM classes in the US are taught in metric (with the exception of aerospace...maybe a few other fields).

Archer, machine screws are dumb. Who the hell decided on the diameter of a 10-24, 8-32, etc? Case in point, a conversation between me and a friend a few days ago:
Him: "hmmmm, should I use a 4-40 for this, or a M2 or M3? Let me see, what's the diameter of an M2?"
Me: "...dude. Seriously? It's an M. 2."
Him: "...oh...right. ...god, that makes SO much more sense! I'm so used to always having to look up diameters!"

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Old 11-10-11, 07:08 PM   #10
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In high energy physics, units become irrelevant and you can set many fundamental constants to 1 unit (you can technically normalize them to anything you want). English/Imperial system of units are illogical and not intuitive.

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Old 11-10-11, 07:25 PM   #11
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In high energy physics, units become irrelevant and you can set many fundamental constants to 1 unit (you can technically normalize them to anything you want). English/Imperial system of units are illogical and not intuitive.
Well, non-dimensionalisation is a standard technique in lots of (all?) scientific fields. Dunno why high energy physics is particular. Anytime you see an equation for a physical problem which is unit-less, it's been non-dimensionalised.

On the subject of units, one of my favourite quotes is from Joe Keller, who said at a special AMS lecture:
Quote:
At first I was especially pleased that this is the fiftieth Gibbs lecture, because 50 is so special in our number system. This is because it is the product of the number of fingers on one hand multiplied by the number of fingers on two hands. But from this point of view, 50 is not a dimensionless number, since it has the dimensions of (fingers per hand) squared. Therefore, its numerical value depends upon the choice of units, so it has no intrinsic significance. This is a reminder that it is only dimensionless numbers which we can regard as large or small, as in the asymptotic analysis I am going to discuss later.

Last edited by Mother Goose; 11-10-11 at 07:33 PM.
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Old 11-10-11, 10:16 PM Thread Starter   #12
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Thanks for the help again guys I ended up getting the answer right after taking a few go overs at it.

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Old 11-11-11, 01:17 AM   #13
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Quote:
Originally Posted by Quigsby View Post
One of the long side is 144 x the hypotenuse. You know that y=24, and x is half the distance between 80 and 60, so it's 10. So square both of those and add them and you get 676, then take the square root and you get 26. So 144x26 = 3744. You've got two of those sides so the long sides total 7488.
I think there is a mistake here. The long side is 24 and the short side is 20. Hence the hypotenuse is [20^2 + 24^2]^0.5 = 31.24

31.24 * 144 = 4498.7
* 2 = 8897.4

So the final SA should be 20997.4.

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Old 11-12-11, 01:21 PM   #14
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Quote:
Originally Posted by Mother Goose View Post
Well, non-dimensionalisation is a standard technique in lots of (all?) scientific fields. Dunno why high energy physics is particular. Anytime you see an equation for a physical problem which is unit-less, it's been non-dimensionalised.
Not necessarily true. In fact the American Physical Society strongly recommends that that you keep the hbar's,c's and epsilons in your work.

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Old 11-12-11, 01:30 PM   #15
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Oh, we get stuck with units a lot in Chemistry. Some of them are pretty standard, SI (or SI-derived) units, but there's a bit of a kcal vs kJ thing going on, which means you need to remember R in both J/K.mol and cal/K.mol ... etc. I was 'brought up' on kcal rather than kJ, which means every time I read a paper in kJ (which I reckon is the 'correct' metric to use), I have to do divisions by 4.18 everywhere.

Then again, I live in Britain where we drive miles at speed miles per hour and fill up our cars with litres of petrol thought of in pounds per litre ...

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Old 11-12-11, 02:04 PM   #16
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Changing over to metric would be great. Except for the fact that you still have to deal with everything that was previously manufactured in standard units. It would be a huge cost to do so in terms of retooling everything that currently uses standard units. We would be looking at a very long conversion process. No matter how much I would want, it isn't like I can just wake up tomorrow and say "I'm going metric and dumping standard units." Sorry to Ronbert for your thread being turned into a "my system is better than yours" cryfest.

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Old 11-12-11, 03:11 PM   #17
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Changing over to metric would be great. Except for the fact that you still have to deal with everything that was previously manufactured in standard units. It would be a huge cost to do so in terms of retooling everything that currently uses standard units. We would be looking at a very long conversion process. No matter how much I would want, it isn't like I can just wake up tomorrow and say "I'm going metric and dumping standard units." Sorry to Ronbert for your thread being turned into a "my system is better than yours" cryfest.
You can. Just throw all of your SAE tools away and use metric. Where metric does not fit use a thumb wrench or a drill and screw extractor

I do it all the time

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Old 11-16-11, 09:28 PM   #18
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When I first read the problem I thought "if only this thing was in metric system..." I mean, is just more easy and logical. They could start with the temperature in weather channels. Is not like a temperature will make adverse effects in people.

Some years ago I read a wikipedia article, when they tried to do this change.

http://en.wikipedia.org/wiki/Metrica..._United_States

Even thought the place I was born uses Fahrenheit I force myself into getting accustomed to Celsius. Using meters instead of feet, still learning Kmph. I'm not talking learning what they mean but the perception of for example, if im going in a car at X speed I know how many mph I'm going without looking at the dashboard, I wanna learn to do the same in Kmph. Right now I can do that in celsius. I know the temperature of my room, without looking at a thermometer.

Bottomline, if everything was metric, everything would make more sense.

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Old 11-17-11, 11:43 AM   #19
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what sucks is i went through grade 8 - my first year in college in canada who uses the metric system and i moved back to the states and now it messes me up allllll the time. i still use Celsius and use my km odometer and i have to suck it up and figure it out and try to do the math all the time.

im up for a petition to send to the senate.... not like it would ever get a head turned though.

p.s. i still spell the word colour and not color.

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Old 11-18-11, 11:16 AM   #20
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What I find annoying, as a pilot, is that the ICAO (International Civil Aviation Organization) refuses to enforce a standard system of units. Airspeed is universally in knots, of course (the one and only imperial unit that kinda makes more sense than it's equivalent in metric), but other than that, anything goes. We use ft for altitude, nautical miles for distance, and inHg for pressure. Everywhere else, they use meters, either nm or km for distance, and Pa for pressure. If you get a weather report for an airport abroad, it'll either come in dual units, or you'll have to convert everything before you plug it into the computer (though I'm sure modern airliners have this capability automatically). Ridiculous. Let's just use metric, for crying out loud.

Though I will admit, I have a hard time figuring out airspeed in km/h. 300-350 knots is a nice cruising speed for a jet, and roughly 100 knots for a piston aircraft. What's that in metric...550-600 km/h, and 180 km/h? I guess that's not too bad to remember...still don't like it.

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