Calculating Dining Corridor Area

Oct 13, 2025 by miodeya.com 38 views

Introduction

Mr. Sharma has a rectangular-shaped plot where he wants to create a pool in the middle and a dining corridor around it. To achieve this, he needs to calculate the area of the dining corridor and determine the quantity of water that can be stored in the pool. In this article, we will delve into the mathematical calculations required to optimize the pool design.

Calculating Dining Corridor Area

To calculate the area of the dining corridor, we need to understand the dimensions of the plot and the pool. Let's assume the length of the plot is L meters, the width is W meters, and the pool is a square with a side length of s meters.

The area of the dining corridor can be calculated by subtracting the area of the pool from the total area of the plot. Mathematically, this can be represented as:

Area of dining corridor = Area of plot - Area of pool

Area of plot = L × W

Area of pool = s²

Substituting these values, we get:

Area of dining corridor = L × W - s²

Now, let's consider the given figure. We can see that the pool is 2 meters deep, but this information is not required to calculate the area of the dining corridor. However, we will use this information later to calculate the quantity of water that can be stored in the pool.

Calculating Quantity of Water in the Pool

To calculate the quantity of water that can be stored in the pool, we need to consider the volume of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

To find the quantity of water that can be stored in the pool, we need to convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, we can multiply the volume by 1000:

Quantity of water = Volume × 1000

Substituting the value of volume, we get:

Quantity of water = s² × 2 × 1000

Now, let's consider the given figure again. We can see that the pool is surrounded by the dining corridor, which has a width of w meters. To calculate the area of the dining corridor, we need to subtract the area of the pool from the total area of the plot. However, we also need to consider the width of the dining corridor.

Calculating Total Area of Plot

To calculate the total area of the plot, we need to consider the length and width of the plot. Let's assume the length of the plot is L meters and the width is W meters. The total area of the plot is:

Total area of plot = L × W

Now, let's consider the width of the dining corridor. We can see that the width of the dining corridor is w meters. To calculate the area of the dining corridor, we need to subtract the area of the pool from the total area of the plot. However, we also need to consider the width of the dining corridor.

Calculating Area of Dining Corridor

To calculate the area of the dining corridor, we need to subtract the area of the pool from the total area of the plot. However, we also need to consider the width of the dining corridor. Mathematically, this can be represented as:

Area of dining corridor = Total area of plot - Area of pool - (2 × w)

Substituting the values, we get:

Area of dining corridor = L × W - s² - (2 × w)

Now, let's consider the given figure again. We can see that the pool is 2 meters deep, and the dining corridor has a width of w meters. To calculate the quantity of water that can be stored in the pool, we need to consider the volume of the pool.

Calculating Quantity of Water in the Pool

To calculate the quantity of water that can be stored in the pool, we need to consider the volume of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

Quantity of water = Volume × 1000

Substituting the value of volume, we get:

Quantity of water = s² × 2 × 1000

Calculating Total Area of Plot

Total area of plot = L × W

Calculating Area of Dining Corridor

Area of dining corridor = Total area of plot - Area of pool - (2 × w)

Substituting the values, we get:

Area of dining corridor = L × W - s² - (2 × w)

Conclusion

In this article, we have calculated the area of the dining corridor and the quantity of water that can be stored in the pool. We have considered the dimensions of the plot and the pool, as well as the width of the dining corridor. By using mathematical formulas and calculations, we have arrived at the following results:

The area of the dining corridor is L × W - s² - (2 × w)
The quantity of water that can be stored in the pool is s² × 2 × 1000

These results provide valuable insights into the design and functionality of the pool and dining corridor. By considering the dimensions and layout of the plot, we can optimize the design to meet the needs of Mr. Sharma and his family.

References

[1] "Mathematics for Engineers and Scientists" by Donald R. Hill
[2] "Geometry and Trigonometry" by Michael Corral
[3] "Mathematics for Calculus" by Michael Corral

Appendix

The following appendix provides additional information and calculations related to the problem.

Calculating Volume of Pool

To calculate the volume of the pool, we need to consider the length, width, and height of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

Quantity of water = Volume × 1000

Substituting the value of volume, we get:

Quantity of water = s² × 2 × 1000

Calculating Area of Dining Corridor

Area of dining corridor = Total area of plot - Area of pool - (2 × w)

Substituting the values, we get:

Area of dining corridor = L × W - s² - (2 × w)

Calculating Quantity of Water in the Pool

To calculate the quantity of water that can be stored in the pool, we need to consider the volume of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

Introduction

In our previous article, we explored the mathematical calculations required to optimize the pool design. We calculated the area of the dining corridor and the quantity of water that can be stored in the pool. In this article, we will address some of the frequently asked questions related to pool design and provide additional insights into the calculations.

Q: What is the formula for calculating the area of the dining corridor?

A: The formula for calculating the area of the dining corridor is:

Area of dining corridor = L × W - s² - (2 × w)

Where L is the length of the plot, W is the width of the plot, s is the side length of the pool, and w is the width of the dining corridor.

Q: How do I calculate the quantity of water that can be stored in the pool?

A: To calculate the quantity of water that can be stored in the pool, you need to consider the volume of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

To find the quantity of water that can be stored in the pool, you need to convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, you can multiply the volume by 1000:

Quantity of water = Volume × 1000

Substituting the value of volume, you get:

Quantity of water = s² × 2 × 1000

Q: What is the significance of the width of the dining corridor in the calculations?

A: The width of the dining corridor is an important factor in the calculations because it affects the area of the dining corridor. When calculating the area of the dining corridor, you need to subtract the area of the pool from the total area of the plot, and then subtract the width of the dining corridor twice (2 × w).

Q: Can I use a different shape for the pool?

A: Yes, you can use a different shape for the pool, but you will need to adjust the calculations accordingly. For example, if the pool is a circle, you will need to use the formula for the area of a circle (A = πr²) to calculate the area of the pool.

Q: How do I ensure that the pool is designed to hold the correct amount of water?

A: To ensure that the pool is designed to hold the correct amount of water, you need to consider the volume of the pool and the quantity of water that can be stored in it. You can use the calculations provided in this article to determine the correct amount of water that the pool can hold.

Q: What are some common mistakes to avoid when designing a pool?

A: Some common mistakes to avoid when designing a pool include:

Not considering the slope of the plot
Not taking into account the width of the dining corridor
Not calculating the correct amount of water that the pool can hold
Not considering the drainage system for the pool

Conclusion

In this article, we have addressed some of the frequently asked questions related to pool design and provided additional insights into the calculations. We hope that this information has been helpful in optimizing your pool design. If you have any further questions or concerns, please do not hesitate to contact us.

References

[1] "Mathematics for Engineers and Scientists" by Donald R. Hill
[2] "Geometry and Trigonometry" by Michael Corral
[3] "Mathematics for Calculus" by Michael Corral

Appendix

The following appendix provides additional information and calculations related to the problem.

Calculating Volume of Pool

To calculate the volume of the pool, you need to consider the length, width, and height of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

Quantity of water = Volume × 1000

Substituting the value of volume, you get:

Quantity of water = s² × 2 × 1000

Calculating Area of Dining Corridor

To calculate the area of the dining corridor, you need to subtract the area of the pool from the total area of the plot. However, you also need to consider the width of the dining corridor. Mathematically, this can be represented as:

Area of dining corridor = Total area of plot - Area of pool - (2 × w)

Substituting the values, you get:

Area of dining corridor = L × W - s² - (2 × w)

Calculating Quantity of Water in the Pool

To calculate the quantity of water that can be stored in the pool, you need to consider the volume of the pool. The volume of a rectangular prism (such as the pool) is given by:

Volume = Length × Width × Height

In this case, the length and width of the pool are equal to the side length s, and the height is 2 meters. Therefore, the volume of the pool is:

Volume = s² × 2

Quantity of water = Volume × 1000

Substituting the value of volume, you get:

Quantity of water = s² × 2 × 1000