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# Volume

Sun 2 Mar, 2014 10:31 pm
A cylindrical oil tank is laying on it's side on a level rack. A stick is placed through a hole in the upper side, and indicates 1 foot of oil in the tank.

Dimensions of tank- diameter- 10 ft. length- 20 ft.

231 cu. in. in a gallon.

Calculate number of gallons of oil in the tank.

X - number of gallons

Volume of a cylinder: [pi]* r^2 * h

3.1416 * 5 * 5 * 20 = 1570.8 cu. ft.

1570.8 / 231 = 6.8

X = 6.8

That is not correct. Where did I make the error(s)?

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Type: Question • Score: 2 • Views: 1,347 • Replies: 14
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BillRM

1
Sun 2 Mar, 2014 10:56 pm
@Randy Dandy,
Lord just to start with cu. inches and cu. feet are not the same unit and one or the other need to be converted to the same units.

Then you have the little matter of the amount of oil in the tank is a fraction of the total tank capacity an so you need to set up an equation to find the amount of oil in the tank.

1
Sun 2 Mar, 2014 11:19 pm
@Randy Dandy,
Another excellent question Randy Dandy.

Did you by any chance get the book "More Mathematical Puzzles of Sam Loyd" as a Christmas or birthday present?

You mentioned in an earlier post that school was long ago , am I right in thinking that you are interested in math puzzles but sometimes struggle with the method of finding the solutions?

I'm an older person who likes mathematical puzzles, can you tell, lol.

Tell me a bit more about you.
Randy Dandy

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Mon 3 Mar, 2014 12:07 am
@BillRM,
Thanks BillRM.
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Randy Dandy

1
Mon 3 Mar, 2014 12:18 am
No, I don't have the book. I saw a similar problem in an old math book.

I have always liked math but struggled in school and still struggle today. In school, when the instructors explained the problems, they looked easy, but when I attempted to solve them, I had difficulty. Thanks.
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BillRM

0
Mon 3 Mar, 2014 12:48 am
@Randy Dandy,
I am getting 2,992 gals in a tank that fully loaded could hold 23,400 gals of oil.

I could had drop a decimal point somewhere as it is late but I think I am in the ball park.

Would explain my thinking but without being able to draw figures it is too hard a task for me to face this AM.
markr

1
Mon 3 Mar, 2014 02:18 pm
@BillRM,
http://mathworld.wolfram.com/CircularSegment.html has the formula for the area of a circular segment (R = 5, h = 1). I get 4.08752772 square feet. Multiplying that by the length of the cylinder gives 81.75055 cubic feet. Google's converter says that's 611.537 gallons. The tank holds 11750.37 gallons.
Randy Dandy

1
Mon 3 Mar, 2014 03:55 pm
@markr,
Thanks markr.
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1
Mon 3 Mar, 2014 11:37 pm
@Randy Dandy,
Randy Dandy this page is a calculator which unsurprisingly comes up with the same answers as markr.

http://www.aqua-calc.com/calculate/volume-in-a-horizontal-cylinder

BillRM

1
Tue 4 Mar, 2014 04:01 am
It kind of taking away some of the fun in not trying to come up with your own equations to deal with such a problem at least in my opinion.

When I get a few minutes, I will go over my approach to the problem and my math.

My equations was somewhat similar to the ones found on the internet and posted here so I think I was on the right track at least.
Randy Dandy

1
Tue 4 Mar, 2014 07:08 pm
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1
Tue 4 Mar, 2014 08:13 pm
@BillRM,
Yes agreed BillRM. Although we may have had quite the wait for me to derive from first principles that the area is :

or the somewhat more elegant :

You should have a look at RandyDandy's other questions BillRM, there are some beauties.

RandyDandy keep posting .
BillRM

1
Tue 4 Mar, 2014 10:02 pm
Getting the answer to the problem is not too hard as it is just two triangles and finding the angle at the center and using that to get the percent of the total area of the circle and then subtracting the area of the two triangles from the sub area of the circle then mult by the length of the cylinder.

It was late when I first try the problem and I somehow decided that the area of a circle was not PI*r^2 but 2*PI*r^2!!!!!!!! so my first results was wrong but setting the problem up was fun.

I thank Randy for posting the problem.
Randy Dandy

1
Wed 5 Mar, 2014 09:04 am
I will keep posting. Thanks.
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Randy Dandy

1
Wed 5 Mar, 2014 09:06 am
@BillRM,
You are welcome, BillRM. Thanks for the kind words.
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