Introduction to Volume
Volume is a scalar quantity indicating the amount of space that a solid figure occupies. Finding the volume of an object can help us figure out how much space it occupies. It also tells us the capacity of that solid or the amount of water needed to be filled in.
The volume of the above figure is 1 cubic unit.
Use of Volume in Daily Life
When you go to fill up your car, the amount of gas in your tank determines how much you pay. You might fill up gas in gallons, whereas someone in the United Kingdom might fill it in liters. “Gallons” and “liters” are known as units. The volume of different containers or solids can be found by using different units. Let us know more about some units of volume measurement.
The Units of Volume Measurement
The volume of a solid is always measured in cubic units. For example, if the dimensions are in meters, the volume will be in cubic meters. In the International System of Units, this is the standard unit of volume (SI). Other units of volume include cubic centimeters, cubic feet, cubic inches, and so on.
What is a Cubic Unit?
Cubic units are units that measure volume in geometry. A cubic unit is the volume of a unit cube whose length, width, and height are all one unit.
Finding the Volume of other Solid Figures Using the Unit Cube
Let us learn by using different examples:
What is the volume of this shape?
This figure is made up of a collection of identical cubes. Let each cube represent 1 unit cube. Now, to find the volume of this shape, we can just count the total number of cubes.
Some Interesting Facts about Volume
- The volume of the cube is equal to the cube of its side length because the cube’s sides are all the same length.
- The formula for finding the volume of a cuboid and a rectangular prism is the same.
Solved Examples
Example 1:
Find the volume of the figure.
Solution:
Each unit cube has an edge length of 1 cm.
So, each unit cube has a volume of 1 cubic centimeter.
The figure is made of 12 unit cubes.
Therefore, the volume of the figure is 12 cubic centimeters.
Example 2:
The Rubix Cube is made up of unit cubes. A box can hold 20 Rubix cubes without any gaps or overlap. What is the volume of the box?
Solution:
The Rubik’s cube is made up of unit cubes that each have an edge length of 1 cm.
So, each unit cube has a volume of 1 cubic centimeter.
One Rubik’s cube is made up of 27 unit cubes.
So, the volume of one Rubik’s cube is = 1 × 27 = 27 cubic centimeters.
Multiply the volume of one Rubik’s cube by the number of Rubik’s cubes that can fit in the box.
20 × 27 = 540
Therefore, the volume of the box is 540 cubic centimeters.
Example 3:
There are no gaps or overlap in a container that holds 27 of the spring toy boxes as shown in the figure below. What is the container’s volume?
Solution:
The spring toy box is made up of unit cubes that each have an edge length of 1 inch
So, each unit cube has a volume of 1 cubic inch.
One spring toy box is made up of 8 unit cubes.
So, the volume of one spring toy box is = 1 × 8 = 8 cubic inches.
Multiply the volume of one toy box by the number of toy boxes that can fit in the container.
27 × 8 = 216
So, the volume of the container is 216 cubic inches.
Volume is a three-dimensional quantity that measures the capacity or space enclosed by a solid shape.
In mathematics, volume is measured in cubic units such as cubic meters, cubic centimeters, and cubic millimeters. Liquid volume is usually expressed in liters or gallons.
In geometry, a unit cube is a cube with each side measuring one unit in length.