109 LearnersLast updated on July 11th, 2025
Volume of Elliptical Cylinder
The volume of an elliptical cylinder is the total space it occupies or the number of cubic units it can hold. An elliptical cylinder is a 3D shape with an elliptical base and a specific height. To find the volume of an elliptical cylinder, we multiply the area of its elliptical base by its height. In real life, kids can relate to the volume of an elliptical cylinder by thinking of objects like a silo with an elliptical cross-section or certain bottles. In this topic, let’s learn about the volume of an elliptical cylinder.
What is the volume of an elliptical cylinder?
The volume of an elliptical cylinder is the amount of space it occupies. It is calculated by using the formula: Volume = π × a × b × h Where 'a' and 'b' are the semi-major and semi-minor axes of the ellipse, and 'h' is the height of the cylinder.
Volume of Elliptical Cylinder Formula An elliptical cylinder is a 3-dimensional shape where the base is an ellipse. To calculate its volume, you multiply the area of the ellipse (π × a × b) by the height of the cylinder.
The formula for the volume of an elliptical cylinder is given as follows: Volume = π × a × b × h
How to Derive the Volume of an Elliptical Cylinder?
To derive the volume of an elliptical cylinder, we use the concept of volume as the total space occupied by a 3D object.
Since the base is an ellipse, its area can be derived as follows:
The formula for the area of an ellipse is: Area = π × a × b For an elliptical cylinder, multiply this area by the height (h) to get the volume: Volume = π × a × b × h
How to find the volume of an elliptical cylinder?
The volume of an elliptical cylinder is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Multiply the area of the elliptical base by the height to find the volume.
Let’s take a look at the formula for finding the volume of an elliptical cylinder: Write down the formula Volume = π × a × b × h 'a' and 'b' are the semi-major and semi-minor axes of the ellipse.
Substitute the values of 'a', 'b', and 'h' into the formula to calculate the volume. To find the volume, multiply the area of the elliptical base by the height.
Tips and Tricks for Calculating the Volume of Elliptical Cylinder
Remember the formula: The formula for the volume of an elliptical cylinder is: Volume = π × a × b × h Break it down:
The volume is how much space fits inside the cylinder. Multiply the area of the elliptical base by the height to find the volume.
Simplify the numbers: If 'a', 'b', and 'h' are simple numbers, it is easy to compute. Use approximations for π When calculating by hand, approximate π as 3.14 or use a calculator for more precision.
Common Mistakes and How to Avoid Them in Volume of Elliptical Cylinder
Making mistakes while learning the volume of an elliptical cylinder is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of elliptical cylinders.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves the lateral and base areas, while volume is calculated by multiplying the base area by the height.
For example, the volume is π × a × b × h, not the surface area formula.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the ellipse's perimeter instead of the volume formula. Volume is the space inside the cylinder, whereas perimeter refers to the total length around the edge of a 2D shape. Do not mix them up.
Mistake 3
Using the wrong Formula for cylindrical volumes
Some kids use the formula for the volume of a circular cylinder (π × r² × h) instead of the elliptical cylinder formula.
Mistake 4
Confusing elliptical measurements with circular ones
Thinking of volume in terms of circular measurements. This happens when someone uses the radius (for circles) instead of the semi-major and semi-minor axes (for ellipses).
Mistake 5
Incorrectly calculating the axes
Some students calculate the given volume with solving for the axes. For example, if the volume is given, and they need to find 'a' or 'b', they might forget to rearrange the volume formula correctly.
Volume of Elliptical Cylinder Examples
Problem 1
An elliptical cylinder has semi-major axis 4 cm, semi-minor axis 3 cm, and height 10 cm. What is its volume?
The volume of the elliptical cylinder is 376.8 cm³.
Explanation
To find the volume of an elliptical cylinder, use the formula: V = π × a × b × h Here, a = 4 cm, b = 3 cm, h = 10 cm,
so: V = π × 4 × 3 × 10 ≈ 376.8 cm³
Problem 2
An elliptical cylinder has semi-major axis 5 m, semi-minor axis 2 m, and height 8 m. Find its volume.
The volume of the elliptical cylinder is approximately 251.2 m³.
Explanation
To find the volume of an elliptical cylinder, use the formula: V = π × a × b × h
Substitute a = 5 m, b = 2 m, h = 8 m: V = π × 5 × 2 × 8 ≈ 251.2 m³
Problem 3
The volume of an elliptical cylinder is 500 cm³, with a semi-major axis of 5 cm and a height of 10 cm. What is the semi-minor axis?
The semi-minor axis of the elliptical cylinder is approximately 3.18 cm.
Explanation
If you know the volume of the elliptical cylinder and need to find the semi-minor axis, rearrange the formula: V = π × a × b × h
Solve for b: b = V / (π × a × h) b = 500 / (π × 5 × 10) ≈ 3.18 cm
Problem 4
An elliptical cylinder has semi-major axis 6 inches, semi-minor axis 3 inches, and height 12 inches. Find its volume.
The volume of the elliptical cylinder is approximately 678.24 inches³.
Explanation
Using the formula for volume: V = π × a × b × h
Substitute a = 6 inches, b = 3 inches, h = 12 inches:
V = π × 6 × 3 × 12 ≈ 678.24 inches³
Problem 5
You have a silo with an elliptical cross-section with a semi-major axis of 7 feet and a semi-minor axis of 4 feet. If the silo is 15 feet tall, how much space (in cubic feet) is available inside?
The silo has a volume of approximately 1319.47 cubic feet.
Explanation
Using the formula for volume: V = π × a × b × h
Substitute a = 7 feet, b = 4 feet, h = 15 feet:
V = π × 7 × 4 × 15 ≈ 1319.47 ft³
FAQs on Volume of Elliptical Cylinder
1.Is the volume of an elliptical cylinder the same as the surface area?
2.How do you find the volume if the axes and height are given?
3.What if I have the volume and need to find one of the axes?
4.Can the axes be decimals or fractions?
5.Is the volume of an elliptical cylinder the same as the surface area?
Important Glossaries for Volume of Elliptical Cylinder
- Semi-major axis: The longest radius of the ellipse forming the base of the elliptical cylinder.
- Semi-minor axis: The shortest radius of the ellipse forming the base of the elliptical cylinder.
- Height: The perpendicular distance between the bases of the elliptical cylinder.
- Volume: The amount of space enclosed within a 3D object. In the case of an elliptical cylinder, the volume is calculated by multiplying the area of the elliptical base by the height.
- Elliptical base: The base of the cylinder, which is an ellipse defined by its semi-major and semi-minor axes.
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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.
Fun Fact
: She has songs for each table which helps her to remember the tables
