Volume Formulas for 3D Shapes (original) (raw)

Last Updated : 23 Jul, 2025

**Volume refers to the amount of space occupied by a three-dimensional object. In geometry, calculating the volume is essential for understanding the capacity of a shape. It is used in various fields like engineering, architecture, and manufacturing to determine the amount of material or space an object can hold.

**Volume formulas are mathematical tools used to calculate the space inside 3D geometric shapes. Each shape, such as a cube, sphere, or cone, has its own specific formula for determining its volume.

Volume Formulas

Volume Formulas Table

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

**Practice Quiz : **Volume Quiz

**Volume of Cube

A cube is a 3D solid whose all sides are equal. Let us consider a cube of side 'a'.

Formula for Volume of Cube****:**

**Volume of Cube (V) = a 3 ,

Where a is Side of Cube.

**The volume **of Cube Using Diagonal:

Volume of Cube(V) = (√3 × d 3 )/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:

• 4 ways to calculate Volume of a cube
• Surface Area of Cube

**Volume of Cuboid

Cuboid is a 3D solid with all three sides length breadth and height are unequal. Consider a cuboid of height h, length l, breadth b.

Formula for **Volume of Cuboid:

**Volume of Cuboid(V) = l × b × h

Where:

• **l is Length of Cuboid
• **b is Breadth of Cuboid
• **h is Height of Cuboid

**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: **Surface Area of Cuboid

**Volume of Cone

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 for Volume of Cone:

**Volume of Cone(V) = πr 2 h/3

Where:

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

Let's consider an example for a 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 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.

Formula for **Volume of Cylinder:

**Volume of Cylinder(V) = πr 2 h

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) = 10 m

Radius of Water Tank (r) = d/2 = 10/2 = 5 m
Amount of water it holds is equal to the volume of water tank

Volume of Water Tank(V) = πr2h

V = 3.14 × (5)2 × (20)
V = 1570 m3

**Learn More: **Surface Area of the Cylinder

**Volume of Sphere

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

**Formula for Volume of Sphere:

**Volume of Sphere = 4/3πr 3

Where, r is the Radius of Sphere.

**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: **Surface Area of Sphere

Volume of Hemisphere

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

Formula for **Volume of Hemisphere:

**Volume of a Hemisphere = 2/3πr 3

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: **Surface Area of Hemisphere

Volume of Prism

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

**Formula for Volume of Prism:

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

**Example: Find the volume of a square prism in which the side of the square base is 8 cm and the 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

Volume of Pyramid

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

**Formula for Volume of Pyramid:

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

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

**Also Read,

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

**Examples 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 we can 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 a hemispherical tub with a radius of 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

**Example 4: **A sphere has a radius of 7 cm. Find its volume.
**Solution:

Given, Radius (r) =7 cm
Volume of a sphere (V) = 4/3πr3

V = 4/3×(3.14)×(7)3
V = 1436.76cm3