109 LearnersLast updated on July 11th, 2025
Volume of 3D Shape
The volume of a 3D shape is the total space it occupies or the number of cubic units it can hold. 3D shapes include cubes, spheres, cylinders, cones, and more, each with its own formula for volume calculation. In real life, kids encounter the concept of volume in various objects, such as water in a bottle, sand in a sandbox, or a ball. In this topic, let’s learn about the volume of different 3D shapes.
What is the volume of a 3D shape?
The volume of a 3D shape is the amount of space it occupies. It is calculated using different formulas depending on the shape.
For example, the volume of a cube is calculated by using the formula: Volume = side³
For a cylinder, the formula is: Volume = π × radius² × height
Each shape has a unique formula based on its dimensions.
How to Derive the Volume of a Sphere?
To derive the volume of a sphere, we use the concept of volume as the total space occupied by a 3D object.
The formula for the volume of a sphere is based on its radius: Volume = (4/3) × π × radius³
This formula is derived from the geometry of a sphere, considering its round shape and uniform radius.
How to find the volume of a cylinder?
The volume of a cylinder is expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
To find the volume, use the formula: Volume = π × radius² × height
First, find the radius and height of the cylinder. Substitute these values into the formula to calculate the volume.
This accounts for the circular base and height of the cylinder.
Tips and Tricks for Calculating the Volume of 3D Shapes
Remember the formulas: Each 3D shape has a specific volume formula. For example, a cube's volume is side³, while a sphere's volume is (4/3)πr³.
Break it down: Understand how each dimension contributes to the volume. For a cylinder, the circular base (radius²) and height are key.
Simplify calculations: Use approximations for π, like 3.14, to make calculations easier.
Check your units: Ensure all measurements are in the same unit before calculating volume.
Common Mistakes and How to Avoid Them in Volume of 3D Shapes
Making mistakes while learning about the volume of 3D shapes is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of different shapes.
Common Mistakes and How to Avoid Them in Volume of 3D Shapes
Making mistakes while learning about the volume of 3D shapes is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of different shapes.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated differently for each shape, whereas volume measures the space inside. Ensure you use the correct formula for each calculation.
Mistake 2
Confusing Volume with Perimeter
Some students may think of the perimeter instead of the volume formula. Volume is the space inside a 3D object, whereas the perimeter refers to the total length around the edges of a 2D shape. Do not mix them up.
Mistake 3
Using the Wrong Formula for Different Shapes
Some students use the incorrect formula for the shape they are calculating. Each 3D shape, like a cylinder or sphere, has its own volume formula. Make sure you use the right one.
Mistake 4
Confusing Linear Measurements with Volume
Thinking of volume in terms of linear measurements. This happens when using the side length or radius without understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly Calculating Dimensions
Some students calculate the given volume without solving for the necessary dimensions first. For instance, if the radius or height is missing, ensure you find these values before calculating volume.
Volume of 3D Shape 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) × π × radius³
Here, the radius is 3 cm, so: V = (4/3) × π × 3³ ≈ 113.1 cm³
Problem 2
A cylinder has a radius of 5 m and a height of 10 m. Find its volume.
The volume of the cylinder is approximately 785.4 m³.
Explanation
To find the volume of a cylinder, use the formula: V = π × radius² × height
Substitute the radius (5 m) and height (10 m): V = π × 5² × 10 ≈ 785.4 m³
Problem 3
The volume of a cube is 216 cm³. What is the side length of the cube?
The side length of the cube is 6 cm.
Explanation
If you know the volume of the cube and need to find the side length, take the cube root of the volume.
Side length = ³√216 = 6 cm
Problem 4
A cone has a radius of 4 inches and a height of 9 inches. Find its volume.
The volume of the cone is approximately 150.8 inches³.
Explanation
Using the formula for the volume of a cone: V = (1/3) × π × radius² × height
Substitute the radius (4 inches) and height (9 inches): V = (1/3) × π × 4² × 9 ≈ 150.8 inches³
Problem 5
You have a rectangular prism with a length of 8 feet, a width of 3 feet, and a height of 2 feet. How much space (in cubic feet) does it occupy?
The rectangular prism has a volume of 48 cubic feet.
Explanation
Using the formula for volume of a rectangular prism: V = Length × Width × Height
Substitute the length (8 feet), width (3 feet), and height (2 feet): V = 8 × 3 × 2 = 48 ft³
FAQs on Volume of 3D Shapes
1.Is the volume of a 3D shape the same as the surface area?
2.How do you find the volume if the dimensions are given?
3.What if I have the volume and need to find a missing dimension?
4.Can dimensions be decimals or fractions?
5.How do units affect volume calculations?
Important Glossaries for Volume of 3D Shape
- Radius: The distance from the center to the edge of a circle or sphere.
- Volume: The amount of space enclosed within a 3D object, expressed in cubic units.
- Cubic Units: The units of measurement used for volume. If dimensions are in meters, the volume will be in cubic meters (m³).
- Height: The perpendicular distance from the base to the top of a 3D shape.
- Pi (π): A mathematical constant approximately equal to 3.14159, used in formulas 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
