Calculating Volume of Water Drawn from a Cylindrical Tank: A Comprehensive Guide

Understanding the calculation of the volume of water drawn from a cylindrical tank is a fundamental concept in many fields, including hydrology, engineering, and environmental science. This article will walk you through the detailed steps and mathematical formulas required to find the volume of water drawn from a tank that changes its water level from 3/4 full to 2/5 full. We will also delve into the conversion of cubic meters to liters, providing a practical example that will help you grasp the concept clearly.

Problem Statement

A cylindrical tank with a radius of 1.4 meters and a height of 1.0 meter is initially 3/4th full of water. After some water is drawn out, the tank is left at 2/5th full. We need to find the volume of the water drawn in liters.

Step-by-Step Solution

Step 1: Calculate the Total Volume of the Tank

The formula for the volume of a cylinder is given by:

Volume (V) πr2h, where r is the radius and h is the height.

Substituting the given dimensions:

V π(1.4m)2(1.0m)

Thus,

V 3.1416 x 1.96 x 1.0 m3

V 6.1575 m3

Step 2: Calculate the Volume of Water Initially in the Tank

The tank is 3/4 full of water:

Volume of water initially in the tank (3/4) x 6.1575 m3

Volume of water initially in the tank 4.6181 m3

Step 3: Calculate the Volume of Water in the Tank After Drawing

The tank is now 2/5 full of water:

Volume of water after drawing (2/5) x 6.1575 m3

Volume of water after drawing 2.4630 m3

Step 4: Calculate the Volume of Water Drawn from the Tank

The volume of water drawn Volume of water initially in the tank - Volume of water after drawing

Volume of water drawn 4.6181 m3 - 2.4630 m3

Volume of water drawn 2.1551 m3

Step 5: Convert Volume from Cubic Meters to Liters

1 cubic meter (m3) is equivalent to 1000 liters (L).

Therefore, the volume of water drawn in liters:

Volume of water drawn 2.1551 m3 x 1000 L/m3

Volume of water drawn 2155.1 liters

Note: Rounding off to the nearest whole number, the volume of water drawn is approximately 2155 liters.

Practical Application and Conversion Factors

Understanding the conversion from cubic meters to liters is crucial in various applications. For instance, 1 cubic meter of water is equivalent to 1000 liters.

To provide a sense of scale, consider a 1 meter cubic tank which holds 1000 liters. For the cylindrical tank with a radius of 1.4 meters and a height of 1.0 meter, its base area is calculated as:

Base area (πr2) π(1.4)2 ≈ 5.911 m2

The total volume of the tank (πr2h) is approximately 5.911 m2 x 1.0 m 5.911 m3, which is close to the 6.1575 m3 we calculated.

When the water is drawn from 3/4 full (4.6181 m3) to 2/5 full (2.4630 m3), the difference in volume is 2.1551 m3, which converts to approximately 2155 liters when converted to liters.

Conclusion: The volume of water drawn from the cylindrical tank is 2155 liters.

Related Questions

Q: Why is it important to convert cubic meters to liters?

A: Converting cubic meters to liters is important as it helps in understanding and expressing the volume of water in a more relatable and widely used unit, making it easier for both professionals and laypeople to comprehend the quantity of water involved.

Q: Can you provide a practical example of the conversion?

A: Consider a cylinder with a volume of 1 cubic meter. It contains 1000 liters of water. When water is drawn from 70% (0.7 m3) to 40% (0.4 m3) of its capacity, the volume drawn is 0.3 m3, which converts to 300 liters.