I need help solving this problem

[ninjagrant]

A truck driver’s gas gauge is broken. He knows he has a 150 gallon cylindrical tank. He takes a stick and inserts into the tank and measures that it was 1/3 high. If he drives 60mph and gets 20 mpg at that speed, how many miles can he travel?

 

[Deleted member 4993]

A truck driver’s gas gauge is broken. He knows he has a 150 gallon cylindrical tank. He takes a stick and inserts into the tank and measures that it was 1/3 high. If he drives 60mph and gets 20 mpg at that speed, how many miles can he travel?

First define the variables from the answers to following questions:

What is the FIND of the problem?​

​

What are the GIVEN conditions of the problem?​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[Steven G]

This is a help site, not a drop off your question and come back later and find the answer website.

 

[Otis]

Hi ninjagrant. There's more than one way to determine the answer (we could use methods from geometry, trigonometry and/or calculus). What math class are you in? Have you learned how to find the cross-sectional area of the fuel against the circular end of the tank (i.e., the area of a circular segment)? The remaining fuel volume is the product of that area times the tank length. Or, maybe you're expected to set up a definite integral? Have they asked for a rounded answer?

Please share your situation, to give us an idea about what you're supposed to do. Thanks!



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[Deleted member 4993]

A truck driver’s gas gauge is broken. He knows he has a 150 gallon cylindrical tank. He takes a stick and inserts into the tank and measures that it was 1/3 high. If he drives 60mph and gets 20 mpg at that speed, how many miles can he travel?

The answer will depend on whether the tank was horizontal or vertical.

 

[Steven G]

The answer will depend on whether the tank was horizontal or vertical.

Good point. I did not think of that. For the record, why does the tank have to be horizontal or vertical?

 

[Deleted member 4993]

Good point. I did not think of that. For the record, why does the tank have to be horizontal or vertical?

My point was that the problem statement provided incomplete initial conditions.

 

[Otis]

The answer will depend on whether the tank [is] horizontal or vertical.

Common sense suggests that the fuel tank is horizontal. It's part of the truck.

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[Dr.Peterson]

I notice that the work (by one method) overlaps considerably with this other recent post:

Partial circumference of a circle

Hello, I'm sure this is easy for y'all, but I can't figure it out. Can you solve for X for the attached?

www.freemathhelp.com

But instead of finding an arc length, you need to find the area of a sector, and subtract a triangle from it.

Of course, I'm making several reasonable assumptions in interpreting the problem.

 

[Deleted member 4993]

The volume of fluid in a partially filled horizontal cylinder =L* [ r^2*cos^{-1} {r − h}/{r} − (r − h)* √{2rh − h^2} ]

Where L = length of the cylinder, r = radius of the cylinder and h = depth of fluid

[ ref: mathsisfun.com/geometry/cylinder-horizontal-volume.html#:~:text=Area Formula&text=b2 = r2 − (r−h)&text=2-,b2 = r2 − (r,2−2rh + h2)]

Assuming the equation above is correct, we would need to calculate the volume of fluid at h = 2*r/3, and continue......

 

[Otis]

Not sure what happened to the OP. Cubist and I used different methods, and we obtained the same answer: 875.3 miles (rounded).

For a fixed volume, the tank's diameter and length are proportional to each other. Therefore, the tank dimensions themselves are arbitrary. I'd picked 2.5 feet for the diameter, followed by using the cylinder-volume formula to calculate the associated length (4.0850 feet). Accordingly, I'd also converted 150 US liquid gallons to cubic feet (shortcut: divide by 7.4805).

I am familiar with the partial-volume formula posted by Subhotosh, so I'd used it to obtain the fuel volume (in cubic feet). After converting back to US liquid gallons (shortcut: multiply by 7.4805), I'd multiplied by 20 because the truck travels 20 miles for each gallon.



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