Volume calculation formula

Introduction

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic meter.

There are arithmetic formulas to find the volume of simple solid shapes, like regular straight edged or circular shapes. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space. (Source: From Wikipedia).


Different types of shapes and formulas for calculating volume


1. Cube = a^3 cubic units, Where a = side of the cube

2. Cuboids = lbh cubic units, where l, b, h are the length, breadth, and height respectively

3. Cylinder = `pi` r^2 h cubic units, where r, h are the radius and height of the cylinder.

4. Pyramid = `(1/3)` bh  cubic units, where b = base area of the pyramid, and h is the height.

5. Cone = `(1/3)`  `pi` r^2h cubic units, where r and h are radius and height of the cone.

6. Sphere = `(4/3)` `pi` r^3 cubic units, where r = radius of the sphere

7. Ellipsoid = `(4/3)` `pi` r1 r2 r3 cubic units, where r1, r2, r3 are the radii of the ellipsoid.


Example for Calculation of the Volumes:


Example 1: Find the volume of a cylindrical canister with radius 10 cm and height 18 cm.

Solution:

Formula for volume calculation: V= ?r^2h

= 3.14 x 102 x 18

= 5652

So, the volume of the canister is 5652 cm^3.


Example 3: Find the volume of a brick 50 cm by 40 cm by 30 cm.

Solution:

Formula for volume calculation: V = lbh

= 50 x 40 x 30

= 60000

So, the volume of the brick is 60000 cm^3