# Calculating Volume of a Gas Tank/Gas within

• marcus768
In summary, the conversation is about a student seeking help with a calculus problem involving finding the volume of gas in a cylindrical tank using an integral. The tank has a radius of 4ft and length of 22ft and is buried on its side. The student is struggling with setting up the integral and getting the correct answer. Another person suggests calculating the area of the wet portion of the end for a given depth and multiplying it by the length of the tank to get the volume. The student is asked to set up the integral for this area.
marcus768

## Homework Statement

I am taking a calc 2 class and I'm studying for finals. I've got this problem i need to figure out and I am having a tough time with it. if someone could give me some guidance in solving this I would greatly appreciate it. I am not looking for answers to this assignment - I would really like to understand how this problem is working, since similar problems will presumably be on the final. If anyone could help guide me through this I would really appreciate it.

A cylindrical gas tank with radius 4ft. and length 22ft is buried on its side.
-Develop an integral that could be used to find the volume of gas in the tank and number of gallons of gas in the tank, given the depth of the gasoline level h
- Test the integral by using it to find the amount of gas in the tank (by vol in cubic ft and gallons) for h=8 ft (full) h=4ft h=0ft h=6 ft

## Homework Equations

I am trying to see if I can set up my integral in a way where it is not dependent on height. V=(pi)(r)^2L is what I have been trying. I am trying to set up my integral in disc format. V=(integral sign) pi[f(x)]^2dx

## The Attempt at a Solution

So what I've been trying to do is first create a function with the V=(pi)(r)^2L formula. Since the radius is given, and the length is given also, where is my variable? Is my radius (4-x)? I guess I am having trouble understanding how to set up the integral. When it comes to evaluating the integral, I am fine. i really need to understand this concept, I am not looking for answers.

any help is appreciated very much, thank you

Suppose you are looking directly at the end of the tank, which is a circle of radius 4. Suppose the water is to depth h. Can you set up an integral to calculate the wet area of the end of the tank? The answer, of course, will depend on h. And the volume of water in the tank is just L times the wet area, no?

Ok, so by using the formula for volume of a cylinder V=pi*(r^2)h
I am coming up with V=pi((4-x)^2)22
I have been trying to use the integral format V=(integral)A(h) dh
I am getting V= (integral evaulated from 0 to 8) (pi(4-x)^2)22
After I evaluate the integral, I am getting approx 2949. This is way off to what it should be, when I use the formula for vol. of a cylinder I get
V= pi(4^2)22 = approx. 1105.
I do not get where I am going wrong!

Did you even read my post? You don't need to integrate the cross section area along the length of the tank. All the cross sections are the same. You need to calculate the area of the wet portion of the end for a depth h and multiply it by the length of the tank to get the volume of water.

Can you set up the integral for the area of the end covered when the water has depth h? That is what you need to do.

## 1. How do you calculate the volume of a gas tank?

To calculate the volume of a gas tank, you need to measure the dimensions of the tank (length, width, and height) in a unit of length (such as meters or inches). Then, use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height of the tank. This will give you the volume of the tank in cubic units.

## 2. What units of measurement should be used for calculating the volume of a gas tank?

The units of measurement used for calculating the volume of a gas tank should be consistent, such as meters, centimeters, or inches. It is important to use the same unit for all dimensions (length, width, and height) to ensure accurate calculations.

## 3. How do you convert the volume of a gas tank from cubic units to gallons?

To convert the volume of a gas tank from cubic units to gallons, you need to know the conversion factor. One cubic foot is equal to 7.48052 gallons. So, to convert from cubic feet to gallons, multiply the volume in cubic feet by 7.48052. For other units, you can use online conversion tools or formulas to convert to cubic feet first and then to gallons.

## 4. Can the volume of a gas tank change due to temperature or pressure?

Yes, the volume of a gas tank can change due to temperature or pressure. According to the Ideal Gas Law (PV = nRT), the volume of a gas is directly proportional to the temperature and inversely proportional to the pressure. This means that as temperature increases, the volume of the gas will also increase, and as pressure increases, the volume will decrease.

## 5. How do you calculate the volume of gas within a gas tank?

To calculate the volume of gas within a gas tank, you need to know the total volume of the tank and the amount of gas in moles (n). Then, use the Ideal Gas Law (PV = nRT) to solve for the volume (V). This will give you the volume of gas within the tank in cubic units. You can then convert to other units of measurement if needed.

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