A Satellite Launch Rocket Has A Cylindrical Fuel Tank. The Fuel Tank Can Hold V V V Cubic Meters Of Fuel. If The Tank Measures D D D Meters Across, What Is The Height Of The Tank In Meters?A. 3 V W \frac{3v}{w} W 3 V B.
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Introduction
When it comes to designing a satellite launch rocket, one of the critical components is the fuel tank. The fuel tank is responsible for storing the fuel that powers the rocket's engines. In this article, we will explore the relationship between the volume of the fuel tank and its dimensions. Specifically, we will calculate the height of a cylindrical fuel tank given its volume and diameter.
The Formula for the Volume of a Cylinder
The volume of a cylinder is given by the formula:
V = πr^2h
where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Calculating the Height of the Fuel Tank
Given that the fuel tank measures d meters across, we can calculate the radius of the tank as follows:
r = d/2
Substituting this value into the formula for the volume of a cylinder, we get:
V = π(d/2)^2h
Simplifying this equation, we get:
V = (πd^2/4)h
To solve for h, we can multiply both sides of the equation by 4 and divide by πd^2:
h = 4V/πd^2
Simplifying the Equation
We can simplify this equation further by using the fact that π is approximately equal to 3.14. Substituting this value into the equation, we get:
h = 4V/3.14d^2
Calculating the Height of the Fuel Tank
Now that we have the equation for the height of the fuel tank, we can use it to calculate the height given the volume and diameter of the tank. For example, if the tank has a volume of 100 cubic meters and a diameter of 2 meters, we can plug these values into the equation:
h = 4(100)/3.14(2)^2
Simplifying this equation, we get:
h = 4(100)/3.14(4)
h = 4(100)/12.56
h = 400/12.56
h = 31.85
Therefore, the height of the fuel tank is approximately 31.85 meters.
Conclusion
In this article, we explored the relationship between the volume of a cylindrical fuel tank and its dimensions. We derived the equation for the height of the tank given its volume and diameter, and used it to calculate the height of a sample tank. This equation can be used to design and optimize the fuel tanks for satellite launch rockets.
Frequently Asked Questions
Q: What is the formula for the volume of a cylinder?
A: The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Q: How do I calculate the radius of the fuel tank?
A: To calculate the radius of the fuel tank, you can divide the diameter of the tank by 2: r = d/2.
Q: What is the equation for the height of the fuel tank?
A: The equation for the height of the fuel tank is h = 4V/πd^2, where V is the volume of the tank and d is the diameter of the tank.
Q: How do I use the equation to calculate the height of the fuel tank?
A: To use the equation to calculate the height of the fuel tank, you can plug in the values for the volume and diameter of the tank, and simplify the equation to get the height.
References
- [1] Wikipedia: Cylinder (geometry)
- [2] Math Open Reference: Cylinder
- [3] Wolfram MathWorld: Cylinder
Further Reading
- [1] NASA: Space Shuttle Main Engines
- [2] SpaceX: Falcon 9 Rocket
- [3] Blue Origin: New Glenn Rocket
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Introduction
In our previous article, we explored the relationship between the volume of a cylindrical fuel tank and its dimensions. We derived the equation for the height of the tank given its volume and diameter, and used it to calculate the height of a sample tank. In this article, we will answer some frequently asked questions about the fuel tank and its dimensions.
Q&A
Q: What is the formula for the volume of a cylinder?
A: The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Q: How do I calculate the radius of the fuel tank?
A: To calculate the radius of the fuel tank, you can divide the diameter of the tank by 2: r = d/2.
Q: What is the equation for the height of the fuel tank?
A: The equation for the height of the fuel tank is h = 4V/πd^2, where V is the volume of the tank and d is the diameter of the tank.
Q: How do I use the equation to calculate the height of the fuel tank?
A: To use the equation to calculate the height of the fuel tank, you can plug in the values for the volume and diameter of the tank, and simplify the equation to get the height.
Q: What is the relationship between the volume and diameter of the fuel tank?
A: The volume of the fuel tank is directly proportional to the square of the diameter. This means that if the diameter of the tank is doubled, the volume will increase by a factor of 4.
Q: How does the height of the fuel tank affect its volume?
A: The height of the fuel tank has a direct relationship with its volume. If the height of the tank is doubled, the volume will also double.
Q: Can I use this equation to calculate the height of a tank with a non-circular cross-section?
A: No, this equation is only applicable to tanks with a circular cross-section. If the tank has a non-circular cross-section, you will need to use a different equation to calculate its height.
Q: What are some real-world applications of this equation?
A: This equation has many real-world applications in the field of aerospace engineering. It can be used to design and optimize the fuel tanks for satellite launch rockets, as well as other types of rockets and spacecraft.
Conclusion
In this article, we answered some frequently asked questions about the fuel tank and its dimensions. We hope that this information has been helpful in understanding the relationship between the volume and diameter of the fuel tank.
Further Reading
- [1] NASA: Space Shuttle Main Engines
- [2] SpaceX: Falcon 9 Rocket
- [3] Blue Origin: New Glenn Rocket
References
- [1] Wikipedia: Cylinder (geometry)
- [2] Math Open Reference: Cylinder
- [3] Wolfram MathWorld: Cylinder
Additional Resources
- [1] Online calculator for calculating the height of a cylinder
- [2] Interactive simulation of a cylinder
- [3] Video tutorial on calculating the height of a cylinder