Volume : Definition, Formula, Examples (original) (raw)

Last Updated : 28 Jan, 2026

Volume of the shape means the capacity of the shape in three-dimensional space.

• The unit of volume is cubic units. For example, cubic meter.
• There are different formulas to calculate volumes of different shapes.
• Volume formulas have many real-life applications, such as finding the volume of containers, the volume of the water tank, and others.

Formulas used to calculate the volume of various figures is shown in the image added below:

Volume of 3D-Shapes

Volume formulas of different solids are given below:

Volume of Cube

A cube is a 3-D shape in which all its dimensions are equal. (i.e. l = b =h). Rubik's cube is a very common example of a cube. A cube of side 'a' is shown in the image below:

Volume of the cube formula is given by:

**Volume of Cube = a 3

where,

• **a is side of a cube

Volume of Cuboid

A cubiod is a 3-D shape in which all its dimensions are different or may be any two are equal. Matchbox is a very common example of cubiod. A cuboid of length 'l', breadth 'b', and height 'h' is shown in the image below:

Volume of cuboid formula is given by:

**Volume of Cuboid = lbh

where,

• **l, **b, **h are the length, breadth and height of cuboid

Volume of Cylinder

Cylinder is a 3-D which have two flat surfaces and a curved surface. Various example of cylinder are, water tankers, pipes, gas cylinders, etc. A cylinder of height 'h' and radius 'r' is shown in the image below:

Volume of cylinder formula is given by:

**Volume of Cylinder = πr 2 h

where,

• **r is radius of cylinder
• **h is height of cylinder

Volume of Sphere

A sphere is a three-dimensional geometric object that is perfectly round in shape, much like a ball. It is defined as the set of all points in three-dimensional space that are equidistant from a fixed point called the center. A sphere of radius 'r' is shown in the image below:

Volume of sphere formula is given by:

**Volume of Sphere = (4 /3)πr 3

where,

• **r is radius of sphere

Volume of Hemisphere

A hemisphere is a three-dimensional geometric shape that is half of a sphere. It is formed by slicing a sphere into two equal parts along a plane passing through its center. A hemisphere of radius 'r' is shown in the image below:

Volume of hemisphere formula is given by:

**Volume of Hemisphere = (2 /3)πr 3

where,

• r is radius of hemisphere.

Volume of Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a single point called the apex or vertex. It resembles a party hat or an ice cream cone. A cone of height 'h' and radius 'r' is shown in the image below:

Volume of cone formula is given by:

**Volume of Cone = (1/3)πr 2 h

where,

• r is radius of cone
• h is height of the cone

Volume of a Pyramid

Pyramid is a three-dimensional geometric shape wich has polygonal base and triangular faces that meet at a common point called the apex. A prramid of height 'h' is shown in the image added below:

Formula for the volume of a pyramid is given as follows,

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

**V = 1/3 A.H cubic units

where,

• V is Volume of Pyramid
• A is Base Area of Pyramid
• H is Height of a Pyramid

List of Volume Formulas

Volume formulas for various figure are added in the table below:

Units of Volume

Volume of any 3-d shape is the space occupied by that shape and is calculated in unit3. The standard unit to measure the side of any 3-d shape is 'm' and so the volume of any 3-d shape is calculated in m3. Other units in which voluemof 3-d shapes is calculated is added in the table below:

Now some times we came across scenarios in which general unit of volume are used and to convert these general unit of volume to standard unit of volume one must go through the table added below:

How to Calculate Volume?

To calculate volume of any 3-d shapes follow the steps added below:

**Step 1: Firstly, identify the shape.

**Step 2: Apply the volume formula of the identified shape. If it is a complex shape divide the same into smaller general shape and yhen apply the volume formula to each dhape.

**Step 3: Simplify the result and add all the volume of smaller shapes if required. Resultant value gives the volume of the given shape.

**Step 4: Use appropriate cubic uniut in the answer to give the exact volume of given shape.

Using these steps one can easily found the volumeof the cube as shown in the examples added below:

**Related:

• Diagonal of a Cube Formula
• Frustum of Cone
• Square Pyramid Formula

Examples on Volume

**Example 1: Find the volume of cube with side 5 units.

**Solution:

Volume of cube is given by:

**Volume of Cube = a 3

V = 53

Volume of Cube = 125 cubic units

**Example 2: Find the volume of cuboid with length, breadth and height as 9, 6 and 5 respectively.

**Solution:

Volume of cuboid is given by:

**Volume of Cuboid = lbh

V = 9 × 6 × 5

Volume of Cuboid = 270 cubic units

**Example 3: Find the volume of cylinder with height 10 units and radius 5 units.

**Solution:

Volume of cylinder is given by:

**Volume of Cylinder = πr 2 h

V = π(5)2 × 10

Volume of Cylinder = 250π cubic units

**Example 4: Find the volume of cone with height and radius as 13 and 6 units respectively.

**Solution:

Volume of cone is given by:

**Volume of Cone = (1 /3)πr 2 h

V = (1 /3)π 62 × 13

V = 12 × 13π

Volume of Cone = 156π cubic units

**Example 5: Find the volume of sphere whose radius is 9 units.

**Solution:

Volume of sphere is given by:

**Volume of Sphere = (4 / 3)πr 3

V = (4 / 3)π 93

V = 4 × 243 × π

Volume of Sphere = 972π cubic units

**Example 6: Find the volume of hemisphere whose radius is 6 units.

**Solution:

Volume of hemisphere is given by:

**Volume of Hemisphere = (2/3)πr 3

V = (2 / 3)π 63

V = 4 × 36π

Volume of Hemisphere = 144π cubic units

Practice Questions on Volume

**Q1. Find the volume of cube with side 13 units.

**Q2. Find the volume of cuboid with length, breadth and height as 19, 8 and 11 respectively.

**Q3. Find the volume of cylinder with height 11 units and radius 7 units.

**Q4. Find the volume of cone with height and radius as 15 and 12 units respectively.

**Q5. Find the volume of sphere whose radius is 4 units.

**Q6. Find the volume of hemisphere whose radius is 7 units.