Volume is the measure of the space enclosed by a three-dimensional object. It tells us how much space a solid shape occupies and is expressed in cubic units. Different three-dimensional shapes have different formulas to calculate their volume based on their dimensions.
Below is the indivudial volume of each shape with solved example to explain the concept better
Volume of Cube
A cube is a 3D solid whose all sides are equal. Let us consider a cube of side 'a'.
.png)
 Formula for Volume of Cube
Volume of Cube (V) = a3
Where a is Side of Cube.
The volume of Cube Using Diagonal:
Volume of Cube
V = \frac{\sqrt{3}d^3}{9} , where, d is Length of Diagonal of Cubes.
Example: Find the volume of a cube if its side is 2 meters.
Given, Side of Cube(a) = 2m
Volume of Cube(V) = a3
V = (2)3 = 8 m3
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.
.png)
Formula for Volume of Cuboid
Volume of Cuboid(V) = l × b × hÂ
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
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) = Ï€r2h/3Â
Where:
- r is Radius of Cone
- h is Height of Cone
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/3V = (3.14 × 30 × 30 × 50)/3
V = 47,100 m3
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) = 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) = 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 tankVolume of Water Tank(V) = πr2h
V = 3.14 × (5)2 × (20)
V = 1570 m3
Volume of Sphere
A sphere is a 3D version of a circle and only has a radius. Let usconsider a sphere of radius r.
Formula for Volume of Sphere
Volume of Sphere = 4/3Ï€r3 Â Â Â
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 mVolume of Sphere  (V) = 4/3πr3
V = 4/3 × (3.14) × (10)3
V = 4186.6 m3
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 = 2/3Ï€r3 Â Â Â
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 mVolume of Hemiphere  (V) = 2/3πr3
V = 2/3 × (3.14) × (10)3
V = 2093.3 m3
Volume of Prism
A prism is a 3-D figurein 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
