Calculating the Volume of Water in a Cylindrical Reservoir

Reservoirs are critical for water management, irrigation, and other practical uses. Understanding how much water a reservoir can store is essential for planning and management purposes. In this article, we will explore how to calculate the volume of a cylindrical reservoir with a 50-meter diameter and 30-meter depth. This calculation is essential for determining the water storage capacity of a reservoir.

Understanding the Reservoir's Shape and Dimensions

Reservoir is defined as a large artificial lake or pond to store water. Often, these reservoirs are in the shape of a cylinder, which is a three-dimensional figure that can be described as a circle extruded along the z-axis.

Key Dimensions

The dimensions provided are:

Diameter: 50 meters Depth: 30 meters

The first step is to calculate the radius of the reservoir, which is half of the diameter.

Calculating the Radius

The radius (r) of the reservoir can be calculated as:

Radius (r) Diameter (d) / 2 50 meters / 2 25 meters

The Volume of a Cylindrical Reservoir

The formula to calculate the volume (V) of a right circular cylinder is:

V πr2h

Here, π (pi) is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height or depth of the cylinder.

Substituting the Values

Let's substitute the values into the formula:

V π(25 meters)2(30 meters)

V π(625 square meters)(30 meters)

V 18750π cubic meters

Calculate the Volume Using a Calculator

Using a calculator, the volume can be calculated as:

V ≈ 18750 * 3.14159 ≈ 59,653.6 cubic meters

Alternative Formula Using Diameter

There is an alternative formula using the diameter (d) instead of the radius (r):

V πd2h / 4

Substituting the values into this formula:

V π(50 meters)2(30 meters) / 4

V π(2500 square meters)(30 meters) / 4

V 75000π cubic meters / 4

V 18750π cubic meters

Using a calculator:

V ≈ 18750 * 3.14159 ≈ 59,653.6 cubic meters

Conclusion

By calculating the volume of a cylindrical reservoir with a 50-meter diameter and 30-meter depth, we find that approximately 59,653.6 cubic meters of water can be stored. This information is crucial for water management and planning.

Related Keywords

reservoir volume cylindrical shape water storage capacity

FAQs

What is the radius if the diameter of the reservoir is 50 meters?

The radius is half of the diameter. Therefore, the radius 50 meters / 2 25 meters.

How is the volume of a cylinder calculated?

The volume of a cylinder is calculated using the formula V πr2h, where r is the radius, and h is the height or depth of the cylinder.

What is the difference between using radius and diameter in volume calculations?

Using the formula V πr2h involves the radius. If you use the diameter, you need to adjust the formula to V πd2h / 4.

References

Math is Fun, "Volume of a Cylinder" - [Link] Jupiter Science, "Cylinder Volume Calculation" - [Link]