A Container Contains 1.6 Litre Of Oil It Has A Rectangular Base Of Length 10 M And Breadth Of 8 M What Is The Height Of The Level Of The Oil In The Container
Introduction
In this article, we will explore the concept of calculating the height of the oil level in a container with a rectangular base. We will use the given dimensions of the container and the volume of oil to determine the height of the oil level.
Understanding the Problem
A container has a rectangular base with a length of 10 m and a breadth of 8 m. The container contains 1.6 litres of oil. We need to find the height of the oil level in the container.
Calculating the Volume of the Container
To calculate the height of the oil level, we first need to calculate the volume of the container. The formula for the volume of a rectangular prism is:
Volume = Length × Breadth × Height
However, we are not given the height of the container. Instead, we are given the volume of oil, which is 1.6 litres. We need to convert this volume to cubic meters to match the units of the container's dimensions.
Converting Litres to Cubic Metres
1 litre is equal to 0.001 cubic metres. Therefore, we can convert 1.6 litres to cubic metres as follows:
1.6 litres × 0.001 cubic metres/litre = 0.0016 cubic metres
Calculating the Height of the Oil Level
Now that we have the volume of the container in cubic metres, we can use the formula for the volume of a rectangular prism to calculate the height of the oil level. We know the length and breadth of the container, and we have calculated the volume of the container.
Let's rearrange the formula for the volume of a rectangular prism to solve for height:
Height = Volume / (Length × Breadth)
Substituting the values we know, we get:
Height = 0.0016 cubic metres / (10 m × 8 m) Height = 0.0016 cubic metres / 80 m² Height = 0.00002 m
Converting the Height to a More Meaningful Unit
The height of the oil level is very small, so it would be more meaningful to express it in millimetres or centimetres. There are 1000 millimetres in a metre, so we can convert the height as follows:
0.00002 m × 1000 mm/m = 0.02 mm
Therefore, the height of the oil level in the container is 0.02 mm.
Conclusion
In this article, we have calculated the height of the oil level in a container with a rectangular base. We used the given dimensions of the container and the volume of oil to determine the height of the oil level. We converted the volume of oil from litres to cubic metres and used the formula for the volume of a rectangular prism to calculate the height of the oil level. The result is a height of 0.02 mm.
Mathematical Formulas Used
- Volume of a rectangular prism: V = l × b × h
- Conversion from litres to cubic metres: 1 litre = 0.001 cubic metres
Real-World Applications
This problem has real-world applications in various fields, such as:
- Engineering: Calculating the height of the oil level in a container is essential in designing and building oil storage tanks.
- Chemistry: Measuring the height of the oil level is crucial in laboratory settings where oil is used as a solvent or reactant.
- Physics: Understanding the concept of volume and height is essential in studying the behavior of fluids and gases.
Tips and Variations
- Using different units: The problem can be solved using different units, such as centimetres or inches, by converting the volume of oil and the dimensions of the container accordingly.
- Adding a layer of oil: If there is a layer of oil on top of the container, the height of the oil level would be different. The problem can be modified to include this additional layer.
- Using a different shape: The problem can be modified to use a different shape, such as a cylinder or a sphere, by using the appropriate formulas for the volume and surface area of the shape.
Frequently Asked Questions (FAQs) =====================================
Q: What is the formula for calculating the height of the oil level in a container?
A: The formula for calculating the height of the oil level in a container is:
Height = Volume / (Length × Breadth)
Q: How do I convert litres to cubic metres?
A: To convert litres to cubic metres, you can use the following conversion factor:
1 litre = 0.001 cubic metres
Q: What if the container has a different shape, such as a cylinder or a sphere?
A: If the container has a different shape, you will need to use a different formula to calculate the height of the oil level. For example, if the container is a cylinder, you can use the formula:
Height = Volume / (π × Radius²)
If the container is a sphere, you can use the formula:
Height = Volume / (4/3 × π × Radius³)
Q: How do I calculate the volume of the container if I don't know the height?
A: If you don't know the height of the container, you can use the formula:
Volume = Length × Breadth × Height
However, if you only know the length and breadth of the container, you will need to use a different approach to calculate the volume. For example, you can use the formula:
Volume = Area × Height
Where Area is the area of the base of the container.
Q: What if there is a layer of oil on top of the container?
A: If there is a layer of oil on top of the container, you will need to add the height of the layer to the height of the oil level. The formula for calculating the height of the oil level in this case is:
Height = (Volume - Layer Volume) / (Length × Breadth)
Q: How do I calculate the volume of the layer of oil?
A: To calculate the volume of the layer of oil, you can use the formula:
Layer Volume = Area × Layer Height
Where Area is the area of the base of the container and Layer Height is the height of the layer of oil.
Q: What if the container is not rectangular?
A: If the container is not rectangular, you will need to use a different approach to calculate the height of the oil level. For example, if the container is a triangle, you can use the formula:
Height = Volume / (Base × Height)
Where Base is the base of the triangle and Height is the height of the triangle.
Q: How do I calculate the height of the oil level if I only know the volume of the oil and the dimensions of the container in different units?
A: If you only know the volume of the oil and the dimensions of the container in different units, you will need to convert the units to match the units of the formula. For example, if the volume of the oil is given in millilitres and the dimensions of the container are given in centimetres, you will need to convert the volume to cubic centimetres and the dimensions to centimetres.
Q: What if I need to calculate the height of the oil level in a container with a non-uniform cross-section?
A: If you need to calculate the height of the oil level in a container with a non-uniform cross-section, you will need to use a different approach to calculate the height of the oil level. For example, you can use the formula:
Height = ∫(Volume / (Length × Breadth)) dx
Where dx is the infinitesimal change in x and ∫ is the integral sign.
Q: How do I calculate the height of the oil level if I have a 3D model of the container?
A: If you have a 3D model of the container, you can use computer-aided design (CAD) software or other 3D modeling tools to calculate the height of the oil level. These tools can help you to visualize the container and calculate the height of the oil level based on the dimensions of the container and the volume of the oil.
Q: What if I need to calculate the height of the oil level in a container with a complex shape?
A: If you need to calculate the height of the oil level in a container with a complex shape, you will need to use a different approach to calculate the height of the oil level. For example, you can use numerical methods such as the finite element method (FEM) or the boundary element method (BEM) to calculate the height of the oil level. These methods can help you to model the complex shape of the container and calculate the height of the oil level based on the dimensions of the container and the volume of the oil.