Volume Formulas for 3D Shapes

Volume Formulas are the formulas that are used to find the volume of various 3-D shapes. Volume of an object is the total space occupied by the object in 3 dimensions. It is measured in cubic centimeters, cubic meters, etc.

In this article, we will learn the Volume formulas of different 3D shapes and their examples in detail.

What is Volume?

The space occupied by an object is the 3-dimension is called the volume of the object. It is also called the capacity of an object and is defined as the total quantity of the material that any object can hold.

For example, the volume of a bucket is the total quantity of water it can hold.

Volume Formulas

Various formulas that are used to calculate the volume of different objects are called the volume formulas It is measured in unit³. If the dimension of an object is given in m, then its volume is measured in m³. The table added below shows the volume formulas of various objects.

Volume Formulas

Volume Formulas Table

The following table contains comprehensive list of all the volume formulas of different 3D shapes

Volume Formulas of 3-Dimensional Shapes
Solid	Volume Formula	Nomenclature of Variables
Cube	a3	a is Side of Cube
Cuboid	l×b×h	l is Length of Cuboid b is Breadth of Cuboid h is Height of Cuboid
Cylinder	πr2h	r is Radius of Base of Cylinder
Sphere	4/3πr3	r is Radius of Sphere
Cone	1/3πr2h	r is Radius of Base of Cone h is Height of Cone
Hemisphere	2/3πr3	r is Radius of Hemisphere
Prism	(A)×(H)	A is Area of base H is Height
Pyramid	1/3 × (A) × (H)	A is Area of Base H is Height

Volume Formulas of 3D Shapes

Volume formulas for various geometric objects and their examples are added below. Learn them in detail for better understanding of the volume of an object.

Volume of Cube Formula

Cube is a 3D solid whose all sides are equal. Let us consider a cube of side ‘a’.

Formula of Cube Volume:

Volume of Cube (V) = a³

where,

• a is Side of Cube

Volume of Cube Using Diagonal:

Volume of Cube(V) = (√3 × d³)/9 

where,

• d is Length of Diagonal of Cube

Let’s consider some examples based on the above formulas.

Example: Find the volume of a cube if its side is 2 meters?

Given,

• Side of Cube(a) = 2 m

Volume of Cube(V) = a³

V = (2)³ = 8 m³

Learn More:

• Volume of Cube
• Surface Area of Cube

Volume of Cuboid Formula

A cuboid is a 3D solid with all three sides length breadth and height are unequal. Let us consider a cuboid of height h, length l, breadth b.

Formula of Cuboid Volume :

Volume of Cubiod(V) = l × b × h 

where,

• l is Length of Cubiod
• b is Breadth of Cubiod
• h is Height of Cubiod

Example: Find the volume of a cuboid of length 10 m height 10 m breadth 20 m.

Solution:

Given,

• Length of Cubiod(l) = 10 m
• Breadth of Cubiod(b) = 10 m
• Height of Cubiod(h) = 20 m

Volume of Cubiod(V) = l.b.h

V = (10)(10)(20)

V = 2,000 m³

Learn More:

• Volume of Cuboid
• Surface Area of Cuboid

Volume of Cone Formula

A cone is a 3D solid with a circular base and a pointy head. Let us consider a cone of height h and base of radius r.

Formula of Cone Volume is,

Volume of Cone(V) = πr²h/3 

Where,

• r is Radius of Cone
• h is Height of Cone

Let’s consider an example for better explanation.

Example: A cone with a radius of 30m and a height of 50 m is filled with water. What amount of water is stored in it.

Solution :

Given,

Radius of cone (r) = 30m

Height of the cone (h) = 50m

 Volume is (V) = πr²h/3

V = (3.14×30×30×50)/3

V = 47,100 m³

Learn More :

• Volume of Cone
• Surface Area of Cone

Volume Formula of Cylinder

A cylinder is a 3D solid with 2 faces as circles and some height. Let us consider a cylinder of base radius r and height h.

Cylinder Volume Formula :

Volume of Cylinder(V) = πr²h

Where,

• r is Radius of Cylinder
• h is Height of Cylinder

Example: A cylindrical water tank is of a height of 20 meters and has a diameter of 10 meters how much water can we hold in this tank?

Solution:

Given,

• Height of Water Tank (h) =20 m
• Diameter of Water Tank (d) =100 m

Radius of Water Tank (r) = d/2 = 100/2 = 50 m

The amount of water it holds is equal to the volume of water tank

Volume of Water Tank(V) = πr²h

V = 3.14(50)²(20)

V = 157000 m³

Learn More:

• Volume of Cylinder
• Surface Area of Cylinder

Volume of Sphere Formula

A sphere is a 3D version of a circle and only has a radius. Let us, consider a sphere of radius r.

Formula of Sphere Volume :

Volume of Sphere = 4/3πr³   

where,

• r is the Radius of Sphere

Let’s consider an example for better explanation.

Example: A spherical balloon with a radius of 10 m is filled with water. What amount of water is stored in it.

Solution:

Given,

• Radius (r) =10 m

Volume of Sphere  (V) = 4/3πr³

V = 4/3×(3.14)×(10)³

V = 4186.6 m³

Learn More:

• Volume of a Sphere
• Surface Area of Sphere

Volume of Hemisphere Formula

A hemisphere is a 3D figure and is half of the sphere it has a radius for its dimension.

Hemisphere Volume Formula:

Volume of a Hemisphere = 2/3πr³   

where,

• r is the Radius of Hemiphere

Example: A hemispherical bowl with a radius of 10 m is filled with water. What amount of water is stored in it?

Given,

• Radius (r) =10 m

Volume of Hemiphere  (V) = 2/3πr³

V = 2/3×(3.14)×(10)³

V = 2093.3 m³

Learn More :

• Volume of Hemiphere
• Surface Area of Hemisphere

Volume of Prism Formula

A prism is a 3-D figures in which the base is a quadrilateral and its faces are triangular and rectangular.

Formula of Prism Volume:

Volume of Prism (V) = (Area of Base) × (Height of Prism)

Example: Find the volume of square prism in which the side of square base is 8 cm and height is 10 cm.

Solution :

Given,

• Side of Square Base (a) = 8 cm
• Height of Prism (H) = 10 cm

Area of Base = a² = (8)² = 64

Volume of Prism(V) = (Area of Base)×(Height of Prism)

V = 64×10 = 640 cm³

Learn More:

• Prism Formula

Volume of Pyramid Formula

A pyramid is a 3-D figures in which the base is triangulae or square and faces are also triangle.

Pyramid Volume Formula:

Volume of Pyramid (V) = 1/3× (Area of Base) × (Height of Pyramid)

Example: Find the volume of square pyramid in which the side of square base is 9 cm and height is 10 cm.

Solution :

Given,

• Side of Square Base (a) = 9 cm
• Height of Pyramid (H) = 10 cm

Area of Base = a² = (9)² = 81

Volume of Pyramid(V) = 1/3 (Area of Base) × (Height of Prism)

V = 27×10 = 270 cm³

Related:

• Cube
• Cylinder
• Right Circular Cone
• Diagonal of a Cube Formula
• Frustum of Cone
• Square Pyramid Formula

Examples on Volume Formula

Let’s solve some questions on the Volume Formulas.

Example 1: Find the volume of a cube if its side is 5 meters?

Solution: 

Given,

• Side = 5 m

V = 5×5×5

V = 125 m³

Example 2: A water tank is of a height of 10 meters and has a diameter of 50 meters, calculate the volume of water can we hold in this tank?

Solution:

Given,

• Height of Water Tank (h) = 10 m
• Diameter of Water Tank (d) = 50 m

Radius of Water Tank (r) = d/2 = 50/2 = 25 m

The amount of water it holds is equal to the volume of water tank

Volume of Water Tank(V) = πr²h

V = 3.14(25)²(10)

V = 19625 m³

Example 3: Calculate the volume of hemispherical tub with radius 14 cm.

Solution:

Given,

• Radius (r) =14 cm

Volume of Hemiphere  (V) = 2/3πr³

V = 2/3×(3.14)×(14)³

V = 5744.10 m³

Practice Questions on Volume Formulas

Q1: Find the Volume of a Cuboidal Tank in Liter whose dimensions are 1m ⨯ 0.5m ⨯ 2m

Q2: Find the volume of cube of side 15 cm.

Q3: Find the volume of a bucket whose radius is 12 cm and height is 14 cm.

Q4: Find the volume of a Conical Tent whose radius is 3 m and height is 4m.

Volume Formulas MCQs Practice Problems

To learn more about Volume Formulas Practice Surface Area and Volume Quiz

Frequently Asked Questions on Volume Formulas

Define Volume of 3D Shapes.

Volume of any object is defined as the total space occupied by any object. It is the total capacity of any object. We can also say that the total material used in making any solid object is the volume of that object.

What is SI unit of Volume?

SI unit of volume is m³. It is also measure in cm³ (cc), ft³ , etc. In general term we measure the volume in litres(l). 1 l = 1000 cc.

What is Volume of Cube Formula?

Formula for Volume of Cube is,

V = a³

What is Volume of Cuboid Formula?

Formula for Volume of Cuboid is,

V = l ⨯ b ⨯ h

What is Volume of Cylinder Formula?

Formula for Volume of Cylinder is,

Volume of Cylinder(V) = πr²h

What is Volume of Cone Formula?

Volume of Cone(V) = 1/3πr²h

What is Volume of Sphere Formula?

Volume of Sphere(V) = 4/3πr³

What is Volume of Hemisphere Formula?

Volume of Hemisphere(V) = 2/3πr³