Volume Formulas

What is Volume?

For any given solid object, the space occupied by such an object is measured and is termed as the volume of the object. Also, if the object is hollow, then the interior is known to be empty. The hollow part can be filled with air or some liquid. In this case, the volume of the substance that can fill the interior will give the capacity of any container.

Therefore, the volume of an object can be defined as the measure of the space it occupies or the capacity of an object is the volume of substance its interior can accommodate. Here, the unit of measurement of either of the two is cubic unit.


Units of Volume

Volume is measured in "cubic" units. The volume of any given figure is the number of cubes required to fill it completely, for example, blocks in a box.

The volume of a cube equals side x side x side. Since each side of a square is equal, it can simply be the length of one side cubed.

If suppose a square has one side of 4 inches, the volume would be 4 inches times 4 inches x 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.)

Some of the formulas to find out volumes of basic geometrical shapes are –


Formulas of Volume of Various Figures

Shapes

Volume Formula

Variables

Rectangular Solid or Cuboid

V = l × w × h

l = Length

w = Width

h = Height

Cube

V = a3

a = Length of edge or side

Cylinder

V = π r2h

r = Radius of the circular base

h = Height

Prism

V = B × h

B = Area of base, (B = side2 or length.breadth)

h = Height

Sphere

V = (4⁄3)π r3

r = Radius of the sphere

Pyramid

V = (1⁄3) × B × h

B = Area of the base,

h = Height of the pyramid

Right Circular Cone

V = (1⁄3)πr2h

r = Radius of the circular base

h = Height

Square or Rectangular Pyramid

V = (1⁄3) × l × w × h

l = Length of the base,

w = Width of base,

h = Height (base to tip)

Ellipsoid

V = (4⁄3) × π × a × b × c

a, b, c = semi-axes of an ellipsoid

Tetrahedron

V = a3⁄ (6 √2)

a = Length of the edge


Solved Examples

Question 1) The dimensions of a rectangular water tank are given as 2m 75cm, 1m 80cm, and 1m 40cm. How many liters of water can be filled in the tank of given measurements?

Solution) As we know that 1m = 100cm.

Dimensions of the tank are given as 2m 75cm, 1m 80cm, and 1m 40cm.

We can write this as 275cm, 180 cm, 140 cm

Now, we know that the volume of the cuboid is, Volume = l × b × h

V = 275 × 180 × 140

V = 6930000 cm3

Since 1000 cm = 1 Liter

Thus, V = 6930 liters

Hence the tank can hold 6930 liters of water.

FAQs (Frequently Asked Questions)

Question 1. What is the Formula for Volume?

Answer: We know that the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

Question 2. What is the Simple Definition of Volume?

Answer: The Simple English Wiktionary has a definition for: volume. The volume of an object is a measure of the amount of space occupied by that object and is not to be confused with mass. The width (or breadth) refers to the size of the object in a direction that is perpendicular to its length.

Question 3. Is Volume a Size?

Answer: Length, area, and volume, Dimensional measures of one-, two-, and three-dimensional geometric objects. All the three mentioned are magnitudes, representing the “size” of an object. Length can be defined as the size of a line segment (see distance formulas), the area is the size of a closed region in a plane, and volume is the size of a solid.