Volume of Three Dimensional Shapes

Volume is how much three-dimensional space a substance or shape occupies or contains. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, can be easily calculated using arithmetic formulas. 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).

Here we are going to see the formulas to find the volume of three dimensional shapes and example problems.
Formulas to Find the Volume of three Dimensional Shapes

Here we are going to see some arithmetic formulas to find the volume of simple three dimensional shapes such as cube, cone, cylinder, and sphere.

Volume of cube = a3 cubic units. Where, a is the side of the cube.
Volume of cone = `1/3 pi r^2 h` cubic units. Where, r and h are the radius and height of the cone.
Volume of cylinder = `pi r^2 h` cubic units. Where, r and h are the radius and height of the cylinder.
Volume of sphere = `4/3 pi r^3` cubic units. Where, r is the radius of the sphere.

Example Problems to Find the Volume of three Dimensional Shapes

Example 1

Find the volume of a three dimensional shape with all sides equal to 3 feet.

Solution

A three dimensional shape with equal sides is a cube.

Volume of a cube = `a^3` cubic units

= 33

= 3 * 3 * 3

= 27

So, the volume of the given three dimensional shape is 27 cubic feet.

Example 2

Find the volume of a sphere, whose radius is 5 m.

Solution

Volume of a sphere = `4/3 pi r^3` cubic units

= `4/3` * 3.14 * `5^3`

= `4/3` * 3.14 * 5 * 5 * 5

= 523.33

The volume of the given sphere is 523.33 cubic meter.

Example 3

Find the volume of a cylinder with radius 3 cm and height 4 cm.

Solution

Volume of a cylinder = `pi r^2 h` cubic units

= 3.14 * 3 * 3 * 4

= 113.04

So, the volume of the given cylinder is 113.04 cubic cm.

Algebra is widely used in day to day activities watch out for my forthcoming posts on equation of line and Distance From a Point to a Line. I am sure they will be helpful.

Example 4

Find the volume of the cone, whose radius is 3 cm and height is 4 cm.

Solution

Volume of a cone = `1/3 pi r^2 h` cubic units

= `1/3` * 3.14 * 3 * 3 * 4

= 3.14 * 3 * 4

= 37.68

So, the volume of the given cone is 37.68 cubic cm.