Calculating the Total Surface Area of a Cylindrical Water Tank

Understanding the total surface area of a cylindrical water tank is crucial for various applications, including structural integrity and material requirements for construction. This article explores the calculation process with a specific example of a cylindrical water tank containing 385,000 liters of water and a height of 10 meters.

Understanding the Volume and Conversion

First, we need to establish the volume of the tank in cubic meters, as the surface area calculations are based on these units.

Given:

Volume, V 385,000 liters Height, h 10 meters

Since 1 liter is equal to 0.001 cubic meters, we convert the volume:

V 385,000 liters x 0.001 m3/liter 385 m3

Calculating the Radius of the Tank

The volume formula for a cylinder is given by:

V π r2h

where (r) is the radius, and (h) is the height of the cylinder.

To find the radius, we rearrange the formula:

r2 V / (π h)

Substituting the known values:

r2 385 / (π x 10) 385 / 31.4159 ≈ 12.26

r ≈ √12.26 ≈ 3.50 meters

Calculating the Total Surface Area

The total surface area (A) of a cylinder is given by:

A 2πrh 2πr2

where:

2πrh is the lateral surface area 2πr2 is the area of the two circular bases

Substituting the known values:

Calculate the lateral surface area:

2πrh 2π(3.50)(10) ≈ 2 x 3.14159 x 3.50 x 10 ≈ 219.91 m2

Calculate the area of the two bases:

2πr2 2π(3.50)2 ≈ 2 x 3.14159 x 12.25 ≈ 76.96 m2

Now combine both areas:

A ≈ 219.91 76.96 ≈ 296.87 m2

Conclusion

The total surface area of the cylindrical water tank is approximately 296.87 square meters. This calculation is fundamental in determining materials needed for the construction and maintenance of cylindrical water tanks.

Additional Considerations

In some cases, such as an open top tank, the total surface area might be slightly different. For example, if the opening at the top is not included in the calculation, the total surface area would be:

Side curved area Circumference × height 2πr × h 2π(0.1107) × 10 ≈ 6.9556 m2

Base area πr2 π(0.1107)2 ≈ 0.0385 m2

Together with the side, the total surface area is approximately 6.9556 0.0385 ≈ 7 m2