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Last updated on July 9th, 2025

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Volume of Circular Tank

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The volume of a circular tank is the total space it occupies or the capacity it can hold. A circular tank is typically cylindrical in shape. To find the volume of a circular tank, we multiply the area of its base by its height. In real life, kids can relate to the volume of a circular tank by thinking of things like a water tank, an oil drum, or a cylindrical container. In this topic, let’s learn about the volume of a circular tank.

Volume of Circular Tank for Canadian Students
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What is the volume of a circular tank?

The volume of a circular tank is the amount of space it occupies. It is calculated using the formula: Volume = π × radius² × height

 

Where ‘radius’ is the distance from the center to the edge of the base of the tank, and 'height' is the vertical distance from the base to the top.

 

Volume of Circular Tank Formula A circular tank is a 3-dimensional shape with a circular base.

 

To calculate its volume, multiply the area of the base (which is π × radius²) by its height.

 

The formula for the volume of a circular tank is given as follows: Volume = π × radius² × height

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How to Derive the Volume of a Circular Tank?

To derive the volume of a circular tank, we use the concept of volume as the total space occupied by a 3D object.

 

Since a circular tank has a circular base, its volume can be derived as follows: The formula for the volume of any cylindrical shape is: Volume = Base Area × Height

 

For a circular base: Base Area = π × radius²

 

Therefore, the volume of a circular tank will be: Volume = π × radius² × height

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How to find the volume of a circular tank?

The volume of a circular tank is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³. Calculate the base area using π × radius², then multiply it by the height to find the volume.

 

Let’s take a look at the formula for finding the volume of a circular tank: Write down the formula Volume = π × radius² × height

 

The radius is the distance from the center of the base to its edge. Once we know the radius and the height, substitute those values into the formula

 

Volume = π × radius² × height

 

To find the volume, calculate the base area and multiply it by the height.

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Tips and Tricks for Calculating the Volume of Circular Tank

  • Remember the formula: The formula for the volume of a circular tank is simple: Volume = π × radius² × height

 

  • Break it down: The volume is how much space fits inside the tank. The base area is π × radius², and you just need to multiply it by the height.

 

  • Simplify the numbers: If the radius is a simple number like 2, 3, or 4, it is easy to calculate. For example, if the radius is 3 and the height is 5, the volume is π × 3² × 5.

 

  • Check for accurate measurements: Ensure you have the correct measurements for both the radius and the height to calculate the volume accurately.
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Common Mistakes and How to Avoid Them in Volume of Circular Tank

Making mistakes while learning the volume of a circular tank is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of circular tanks.

Mistake 1

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Confusing Volume with Surface Area

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Some students confuse the formula for volume with the formula for surface area. Surface area is calculated differently, but volume is calculated by using the base area and height. For example, the volume is π × radius² × height, not the surface area formula.

Mistake 2

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Confusing Volume with Circumference

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Some kids may think of the tank’s circumference instead of the volume formula. Volume is the space inside the tank, whereas circumference refers to the distance around the base. Do not mix them up.

Mistake 3

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Using the wrong Formula for different shapes

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Some kids use the formula for the volume of other shapes, such as cubes or rectangular prisms, instead of the circular tank formula.

Mistake 4

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Confusing cubic volume with linear volume

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Thinking of volume in terms of linear measurements. This happens when someone uses linear measurements like diameter without squaring the radius for the base area.

Mistake 5

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Incorrectly calculating the radius

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Some students make mistakes when solving for the radius. For example, if diameter is given, they might forget to divide by two to find the radius before using the formula.

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Volume of Circular Tank Examples

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Problem 1

A circular tank has a radius of 4 m and a height of 10 m. What is its volume?

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The volume of the circular tank is approximately 502.65 m³.

Explanation

To find the volume of a circular tank, use the formula: V = π × radius² × height

 

Here, the radius is 4 m and the height is 10 m, so: V = π × 4² × 10 ≈ 502.65 m³

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Problem 2

A circular tank has a diameter of 6 cm and a height of 12 cm. Find its volume.

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The volume of the circular tank is approximately 339.12 cm³.

Explanation

First, find the radius: Radius = Diameter/2 = 6 cm/2 = 3 cm

 

Then use the formula: V = π × radius² × height

 

Substitute the radius (3 cm) and height (12 cm): V = π × 3² × 12 ≈ 339.12 cm³

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Problem 3

The volume of a circular tank is 785.4 m³, and its height is 5 m. What is the radius of the tank?

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The radius of the tank is approximately 7 m.

Explanation

To find the radius given the volume and height, rearrange the formula: Volume = π × radius² × height

 

785.4 = π × radius² × 5

 

Radius² = 785.4/(π × 5) Radius ≈ 7 m

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Problem 4

A circular tank has a radius of 2.5 inches and a height of 8 inches. Find its volume.

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The volume of the circular tank is approximately 157.08 inches³.

Explanation

Using the formula for volume: V = π × radius² × height

 

Substitute the radius (2.5 inches) and height (8 inches): V = π × 2.5² × 8 ≈ 157.08 inches³

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Problem 5

You have a circular tank with a radius of 3 feet and a height of 6 feet. How much space (in cubic feet) is available inside the tank?

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The tank has a volume of approximately 169.65 cubic feet.

Explanation

Using the formula for volume: V = π × radius² × height

 

Substitute the radius (3 feet) and height (6 feet): V = π × 3² × 6 ≈ 169.65 ft³

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FAQs on Volume of Circular Tank

1.Is the volume of a circular tank the same as the surface area?

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2.How do you find the volume if the radius and height are given?

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3.What if I have the volume and need to find the radius?

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4.Can the radius be a decimal or fraction?

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5.Is the volume of a circular tank the same as the surface area?

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Important Glossaries for Volume of Circular Tank

  • Radius: The distance from the center to the edge of the base of the circular tank.

 

  • Height: The vertical distance from the base to the top of the tank.

 

  • Volume: The amount of space enclosed within a 3D object. In the case of a circular tank, the volume is calculated using the base area and height.

 

  • Cubic units: The units of measurement used for volume. If the radius and height are in meters, the volume will be in cubic meters (m³).

 

  • Base Area: The area of the circular base of the tank, calculated as π × radius².
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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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