Math K-Plus

How To Find The Volume Of Geometric Shapes

How To Find The Volume Of Three Dimensional Shapes (3D Shapes)

What is the definition of Volume? In geometry, the volume of a three dimensional shape (a shape with length and width and height), is the total interior space of the shape. If you filled the shape below with water, how much can it hold? The unit of measurement for Volume of a shape may be any of the following: cubic inches, cubic feet, cubic centimeters, cubic meters, cubic kilometers, etc.

Let us look at a real example. Picture the diagram below as a plastic box with no lid i.e. a cubic container where all lengths are the same. Our goal is to fill the container to the very top with water and, we want known how much water is in the container. To make the problem easier we assume all sides of this particular container are 10 inches in length. In other words, the length, width, and height are each ten inches. The Volume of the container is equal to length times the width times the height. If the length is 10 inches and the width is 10 inches, and height are 10 inches then the volume equals 1,000 cubic inches (10 inches × 10 inches × 10 inches = (10 inches)3 = 1,000 cubic inches = 1,000 inches3 = 1,000 in3).

When we say cubic inches, picture solid blocks that are one inch in length, width, and height; we could stack 1,000 of these blocks in the 10 by 10 by 10 inch container talked about above.

Volume Formula
Formula = Side × Side × Side =
Formula = S × S × S =
Formula = S3