116 LearnersLast updated on July 11th, 2025
Volume of Conical Tank
The volume of a conical tank is the total space it occupies or the number of cubic units it can hold. A conical tank is a 3D shape with a circular base that tapers smoothly from a flat base to a point called the apex. To find the volume of a conical tank, we use the formula that incorporates the radius of its base and its height. In real life, conical tanks are used for storing liquids, and they can be related to objects like funnels or ice cream cones. In this topic, let’s learn about the volume of a conical tank.
What is the volume of the conical tank?
The volume of a conical tank is the amount of space it occupies. It is calculated by using the formula: Volume = (1/3)πr²h Where ‘r’ is the radius of the base, and ‘h’ is the height of the cone.
Volume of Conical Tank Formula A conical tank is a 3-dimensional shape with a circular base and a pointed top.
To calculate its volume, you multiply the area of the base (πr²) by the height (h) and then take one-third of that product.
The formula for the volume of a conical tank is given as follows: Volume = (1/3)πr²h
How to Derive the Volume of a Conical Tank?
To derive the volume of a conical tank, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows:
The formula for the volume of a cylinder is: Volume = Base Area x Height For a cone,
the volume is one-third of the equivalent cylinder: Volume = (1/3) x Base Area x Height
Since the base area of the cone is a circle, its area is πr². Therefore, Volume = (1/3)πr²h
How to find the volume of a conical tank?
The volume of a conical tank is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Use the radius of the base and the height of the cone in the formula to find the volume.
Let’s take a look at the formula for finding the volume of a conical tank: Write down the formula Volume = (1/3)πr²h
Substitute the radius and height into the formula. Once you know the radius and height, substitute those values into the formula.
To find the volume, calculate the base area (πr²), multiply by the height, and then divide by 3.
Tips and Tricks for Calculating the Volume of a Conical Tank
Remember the formula: The formula for the volume of a conical tank is: Volume = (1/3)πr²h
Break it down: The volume is how much space fits inside the conical tank. You need to calculate the area of the base first, multiply by the height, and then divide by three.
Simplify the numbers: If the numbers for the radius and height are simple like 2, 3, or 4, it is easy to calculate the volume.
Check for cube roots: If you are given the volume and need to find the height or radius, you might need to rearrange the formula to solve for the unknown.
Common Mistakes and How to Avoid Them in Volume of Conical Tank
Making mistakes while learning the volume of the conical tank is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of conical tanks.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves both the base and the slant height, but volume is calculated by using the base radius and height.
For example, the volume is (1/3)πr²h, not the surface area formula.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of the base instead of the volume formula. Volume is the space inside the conical tank, whereas perimeter refers to the total length around the base of the cone. Do not mix them up.
Mistake 3
Using the wrong formula for cylinders
Some kids use the formula for the volume of a cylinder (πr²h) instead of the cone formula (1/3)πr²h. Remember, the volume of a cone is a third of the volume of a cylinder with the same base and height.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone uses the radius or height (which are linear measurements) without understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the radius or height
Some students calculate the given volume with solving for the radius or height. For example, if the volume is given, and they need to find the radius, they might forget to rearrange the formula correctly to solve for the unknown.
Volume of Conical Tank Examples
Problem 1
A conical tank has a base radius of 3m and a height of 6m. What is its volume?
The volume of the conical tank is 56.52 m³.
Explanation
To find the volume of a conical tank, use the formula: V = (1/3)πr²h Here, the radius is 3m and the height is 6m,
so: V = (1/3)π(3)²(6) = (1/3)π(9)(6) = (1/3)(54)π ≈ 56.52 m³
Problem 2
A conical tank has a base radius of 5 ft and a height of 10 ft. Find its volume.
The volume of the conical tank is approximately 261.80 ft³.
Explanation
To find the volume of a conical tank, use the formula: V = (1/3)πr²h Substitute the radius (5 ft) and height (10 ft):
V = (1/3)π(5)²(10) = (1/3)π(25)(10) = (1/3)(250)π ≈ 261.80 ft³
Problem 3
The volume of a conical tank is 100 cm³. The base radius is 4 cm. What is the height of the tank?
The height of the conical tank is approximately 5.97 cm.
Explanation
If you know the volume of the conical tank and the radius, rearrange the formula to solve for the height:
V = (1/3)πr²h 100 = (1/3)π(4)²h 100 = (1/3)π(16)h 100 = (16/3)πh h ≈ 5.97 cm
Problem 4
A conical tank has a base radius of 2.5 inches and a height of 7 inches. Find its volume.
The volume of the conical tank is approximately 45.83 inches³.
Explanation
Using the formula for volume: V = (1/3)πr²h
Substitute the radius (2.5 inches) and height (7 inches):
V = (1/3)π(2.5)²(7) ≈ 45.83 inches³
Problem 5
You have a conical tank with a base radius of 6 feet and a height of 9 feet. How much space (in cubic feet) is available inside the tank?
The tank has a volume of approximately 339.12 cubic feet.
Explanation
Using the formula for volume: V = (1/3)πr²h
Substitute the radius (6 feet) and height (9 feet):
V = (1/3)π(6)²(9) = (1/3)π(36)(9) = (1/3)(324)π ≈ 339.12 ft³
FAQs on Volume of Conical Tank
1.Is the volume of a conical tank the same as the surface area?
2.How do you find the volume if the radius and height are given?
3.What if I have the volume and need to find the radius or height?
4.Can the radius or height be a decimal or fraction?
5.Is the volume of a conical tank the same as the surface area?
Important Glossaries for Volume of Conical Tank
- Radius: The distance from the center of the base to its edge.
- Height: The perpendicular distance from the base to the apex of the cone.
- Volume: The amount of space enclosed within a 3D object. In the case of a conical tank, the volume is calculated by using the formula (1/3)πr²h.
- Cubic Units: The units of measurement used for volume. If the radius and height are in meters (m), the volume will be in cubic meters (m³).
- Base Area: The area of the circular base of the cone, calculated as πr².
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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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