Volume of the shape means the capacity of the shape. To calculate volumes of different shapes we have different formulas. The basic formula for volume is obtained by multiplying length, breadth and height.

In this article, we will explore how to calculate volumes for different shapes. Also, we will solve some examples related to how to calculate volumes.

Volume Definition

Volume is the measure of the region covered by the 3-D solids. In other words, volume is defined as the capacity of a closed surface in three-dimensional space. The unit of volume is cubic units. The volume of various figures is used for various purposes. Volume formulas also have real-life applications, such as finding the volume of containers, the volume of the water tank, and others.

Volumes Formulas for Various Shapes

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 = a³

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 = πr²h

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)πr³

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)πr³

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)πr² 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: