110 LearnersLast updated on July 11th, 2025
Volume of Oval
The volume of an oval, specifically an ellipsoid, is the total space it occupies in a 3D space. An ellipsoid is a three-dimensional shape that resembles a stretched or squished sphere. To find the volume of an ellipsoid, we use the formula involving its three axes. In real life, the volume of an oval can be related to objects like eggs or rugby balls. In this topic, let’s learn about the volume of an oval.
What is the volume of an oval?
The volume of an oval (ellipsoid) is the amount of space it occupies. It is calculated using the formula: Volume = (4/3)πabc Where 'a', 'b', and 'c' are the lengths of the semi-principal axes of the ellipsoid.
Volume of Oval Formula An ellipsoid is a 3-dimensional shape with three perpendicular axes of different lengths. To calculate its volume, multiply the lengths of its axes and apply the constant (4/3)π.
The formula for the volume of an ellipsoid is: Volume = (4/3)πabc
How to Derive the Volume of an Oval?
To derive the volume of an ellipsoid, we consider it as a stretched sphere. The formula for the volume of a sphere is: Volume = (4/3)πr³
For an ellipsoid: Replace the radius 'r' with the semi-principal axes 'a', 'b', and 'c'.
The volume of an ellipsoid is: Volume = (4/3)πabc
How to find the volume of an oval?
The volume of an ellipsoid is expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). Multiply the lengths of the semi-principal axes and apply the constant (4/3)π to find the volume.
Let’s take a look at the formula for finding the volume of an ellipsoid: Write down the formula: Volume = (4/3)πabc 'a', 'b', and 'c' are the lengths of the semi-principal axes of the ellipsoid.
Once you know the lengths of the axes, substitute those values into the formula Volume = (4/3)πabc To find the volume, multiply the semi-principal axes and apply the constant.
Tips and Tricks for Calculating the Volume of Oval
Remember the formula: The formula for the volume of an ellipsoid is: Volume = (4/3)πabc Break it down: The volume is the space inside the ellipsoid. You need to multiply the lengths of its axes and apply the constant.
Simplify the numbers: If the axes lengths are simple numbers, it is easy to calculate. For example, if a = 2, b = 3, and c = 4, the volume is (4/3)π(2)(3)(4).
Check for consistency: Ensure the axes are measured in the same units before calculating the volume.
Common Mistakes and How to Avoid Them in Volume of Oval
Making mistakes while learning the volume of an ellipsoid is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of ellipsoids.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is more complex for ellipsoids, but volume is calculated by multiplying the semi-principal axes and applying the constant (4/3)π. For example, volume is (4/3)πabc.
Mistake 2
Using the wrong formula for different shapes
Some students might use the formula for the volume of a sphere or cylinder instead of the ellipsoid formula.
Mistake 3
Confusing axes lengths
Mixing up the lengths of the semi-principal axes 'a', 'b', and 'c' can lead to incorrect calculations of volume.
Mistake 4
Incorrectly calculating the volume
Errors can occur when multiplying the lengths of the axes or applying the constant (4/3)π incorrectly.
Mistake 5
Ignoring the constant
Forgetting to multiply by (4/3)π can lead to incorrect volume calculations.
Volume of Oval Examples
Problem 1
An ellipsoid has semi-principal axes of lengths 2 cm, 3 cm, and 4 cm. What is its volume?
The volume of the ellipsoid is approximately 100.53 cm³.
Explanation
To find the volume of an ellipsoid, use the formula: V = (4/3)πabc Here, a = 2 cm, b = 3 cm, c = 4 cm, so: V = (4/3)π(2)(3)(4) ≈ 100.53 cm³
Problem 2
An ellipsoid has semi-principal axes of lengths 5 m, 6 m, and 7 m. Find its volume.
The volume of the ellipsoid is approximately 879.65 m³.
Explanation
To find the volume of an ellipsoid, use the formula: V = (4/3)πabc
Substitute the axes lengths (a = 5 m, b = 6 m, c = 7 m): V = (4/3)π(5)(6)(7) ≈ 879.65 m³
Problem 3
The volume of an ellipsoid is 523.6 cm³. If two of its semi-principal axes are 6 cm and 5 cm, what is the length of the third axis?
The length of the third axis is approximately 2.8 cm.
Explanation
Given the volume V = 523.6 cm³ and axes a = 6 cm, b = 5 cm,
use the formula: V = (4/3)πabc 523.6 = (4/3)π(6)(5)c Solve for 'c': c ≈ 2.8 cm
Problem 4
An ellipsoid has semi-principal axes of lengths 1.5 inches, 2 inches, and 2.5 inches. Find its volume.
The volume of the ellipsoid is approximately 31.42 inches³.
Explanation
Using the formula for volume: V = (4/3)πabc
Substitute the axes lengths (a = 1.5 inches, b = 2 inches, c = 2.5 inches):
V = (4/3)π(1.5)(2)(2.5) ≈ 31.42 inches³
Problem 5
You have an ellipsoid with semi-principal axes of 3 feet, 4 feet, and 5 feet. How much space (in cubic feet) is available inside the ellipsoid?
The ellipsoid has a volume of approximately 251.33 cubic feet.
Explanation
Using the formula for volume: V = (4/3)πabc
Substitute the axes lengths (a = 3 feet, b = 4 feet, c = 5 feet):
V = (4/3)π(3)(4)(5) ≈ 251.33 ft³
FAQs on Volume of Oval
1.Is the volume of an oval the same as the surface area?
2.How do you find the volume if the axes lengths are given?
3.What if I have the volume and need to find an axis length?
4.Can the axes lengths be decimals or fractions?
5.Is the volume of an oval the same as the surface area?
Important Glossaries for Volume of Oval
- Semi-principal axes: The three perpendicular axes of an ellipsoid, denoted as a, b, and c.
- Ellipsoid: A 3D shape resembling a stretched or squished sphere, defined by its semi-principal axes.
- Volume: The amount of space enclosed within a 3D object. For an ellipsoid, it is calculated using the formula (4/3)πabc.
- Cubic units: The units of measurement used for volume. If the axes are in centimeters, the volume will be in cubic centimeters (cm³).
- Pi (π): A mathematical constant used in the formulas for volumes and surface areas of circular and spherical shapes, approximately equal to 3.14159.
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
