Volume is a measurement of the amount of space that 3-d objects holds. For example, if a question on the GED math test asked you to calculate the volume of a cup, you can’t just say how many ounces it holds. You need to say how many cubes of a unit, like cubic inches, fit into the cup. For this reason volume is always represented in cubic units, such as 5 yards³.
Volume of a Cube
Volume = edge³
To find the volume of a cube, just cube the length of the edge. Cubing something just means multiplying it by itself two times. In the example above you would just multiply 5 by itself two times:
5³ = 5 x 5 x 5 = 125 in.³ (or 125 cubic inches)
Volume of a Rectangular Container
Volume = length x height x width
To find the volume of a rectangular container, multiply its length by its height by its width. If you were asked to find the volume of the above rectangular solid, just multiply 4 by 2 by 1.5.
4 x 2 = 8
8 x 1.5 = 12
volume = 12 ft.³
Volume of a Cylinder
Volume = π x radius² x height
To find the volume of a cylinder, square the radius, multiply that by the height, and multiply that by pi.
2² = 4
4 x 4 = 16
16 x π (3.14) = 50.24
v = 50.24 cm³
Volume of a Pyramid
Volume = 1/3 x (base edge)² x height
To find a square base pyramid’s volume, first square the length of one of its base sides, multiply that by its height, and multiply that number by a third (1/3).
3² = 9
9 x 5 = 45
45 x 1/3 = 15
v = 15 ft³
Volume of a Cone
Volume = 1/3 x π x radius² x height
Square the radius, multiply that by the cone’s height, multiply by pi, then multiply by 1/3.
3² = 9
9 x 7 = 63
63 x π (3.14) = 197.82
197.82 x 1/3 = 65.94
v = 65.94 cm³