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127 LearnersLast updated on December 11, 2025
Volume of Solid Sphere
The volume of a solid sphere is the total space it occupies or the number of cubic units it can hold. A sphere is a 3D shape where every point on its surface is equidistant from its center. To find the volume of a sphere, we use the formula involving its radius. In real life, kids relate to the volume of a sphere by thinking of things like a basketball, a globe, or a marble. In this topic, letโs learn about the volume of a solid sphere.
What is the volume of a solid sphere?
The volume of a solid sphere is the amount of space it occupies.
It is calculated by using the formula: Volume = (4/3)πr³ Where ‘r’ is the radius of the sphere.
Volume of Sphere Formula : A sphere is a 3-dimensional shape where the distance from the center to any point on the surface is the same.
To calculate its volume, we use the radius of the sphere in the formula. The formula for the volume of a sphere is given as follows: Volume = (4/3)πr³
How to Derive the Volume of a Solid Sphere?
To derive the volume of a solid sphere, we use the concept of volume as the total space occupied by a 3D object.
The volume is derived using integration, but it can also be understood as follows:
The formula for the volume of a sphere is: Volume = (4/3)πr³
This formula comes from integrating the cross-sectional area of circles across the radius of the sphere.
How to find the volume of a solid sphere?
The volume of a sphere is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³. Use the radius of the sphere to calculate its volume.
Let’s take a look at the formula for finding the volume of a sphere: Write down the formula Volume = (4/3)πr³
The radius is the distance from the center of the sphere to any point on its surface. This is the only measurement needed to calculate the volume.
Once we know the radius, substitute that value for ‘r’ in the formula: Volume = (4/3)πr³
To find the volume, cube the radius, then multiply by π and 4/3.
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Tips and Tricks for Calculating the Volume of Solid Sphere
Remember the formula: The formula for the volume of a solid sphere is simple: Volume = (4/3)πr³
Break it down: The volume is how much space fits inside the sphere. You just need to cube the radius and multiply it by π and 4/3.
Simplify the numbers: If the radius is a simple number like 2, 3, or 4, it is easy to cube. For example, if r=3, then r³=27.
Check for accuracy: Ensure you use the correct value for π, often approximated as 3.14159, to achieve accurate results.
Common Mistakes and How to Avoid Them in Volume of Solid Sphere
Making mistakes while learning the volume of the solid sphere is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of spheres.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by 4πr², but volume is calculated by (4/3)πr³. For example, the volume is (4/3)πr³, not 4πr².
Mistake 2
Using Diameter Instead of Radius
Some kids may use the diameter instead of the radius in the formula. Remember, the radius is half of the diameter. The formula requires the radius.
Mistake 3
Ignoring the Fraction in the Formula
Some kids use the formula for the volume of a sphere but forget to divide by 3, using 4πr³ instead of (4/3)πr³.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone uses linear distance instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the radius
Some students calculate the given volume without solving for the radius. For example, if the volume is given, and they need to find the radius, they might forget to take the cube root of the result after manipulating the formula.
Volume of Solid Sphere Examples
Problem 1
A sphere has a radius of 3 cm. What is its volume?
The volume of the sphere is approximately 113.1 cm³.
Explanation
To find the volume of a sphere, use the formula: V = (4/3)πr³
Here, the radius is 3 cm, so: V = (4/3)π(3)³ ≈ 113.1 cm³
Problem 2
A sphere has a radius of 6 m. Find its volume.
The volume of the sphere is approximately 904.78 m³.
Explanation
To find the volume of a sphere, use the formula: V = (4/3)πr³
Substitute the radius (6 m): V = (4/3)π(6)³ ≈ 904.78 m³
Problem 3
The volume of a sphere is 288ฯ cmยณ. What is the radius of the sphere?
The radius of the sphere is 6 cm.
Explanation
If you know the volume of the sphere, and you need to find the radius, you’ll rearrange the formula to solve for r.
288π = (4/3)πr³
r³ = (288 × 3) / 4
r = 6 cm
Problem 4
A sphere has a radius of 1.5 inches. Find its volume.
The volume of the sphere is approximately 14.137 inches³.
Explanation
Using the formula for volume: V = (4/3)πr³
Substitute the radius 1.5 inches: V = (4/3)π(1.5)³ ≈ 14.137 inches³
Problem 5
You have a spherical balloon with a radius of 5 feet. How much space (in cubic feet) does it occupy?
The balloon has a volume of approximately 523.6 cubic feet.
Explanation
Using the formula for volume: V = (4/3)πr³
Substitute the radius 5 feet: V = (4/3)π(5)³ ≈ 523.6 ft³
FAQs on Volume of Solid Sphere
1.Is the volume of a sphere the same as the surface area?
2.How do you find the volume if the radius is given?
3.What if I have the volume and need to find the radius?
4.Can the radius be a decimal or fraction?
5.Does the volume of a sphere change if the radius changes?
Important Glossaries for Volume of Solid Sphere
- Radius: The distance from the center of the sphere to any point on its surface.
- Volume: The amount of space enclosed within a 3D object. In the case of a sphere, the volume is calculated using the formula (4/3)πr³.
- Cubic units: The units of measurement used for volume. If the radius is in centimeters (cm), the volume will be cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
- Surface area: The total area covered by the surface of the sphere, calculated as 4πr².
- π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles and spheres.
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
