Volumes of Cubes, Cuboids, Cylinders and Prisms

The volume of a shape measures the three dimensional (3D) amount of space it takes up.

Different shapes have different ways to find the volume.

Remember

The volume of solid objects is measured in cubic units. The most important thing to remember when calculating volume is that all the dimensions must be in the same units.

Volumes of Cubes

Recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice.

Or as a formula:

\(V=a^{3}\)

where \(a\) is the length of each side of the cube.

Volume Cuboids

Volume of a cuboid = (length × breadth × height) cubic units. = (l × b × h) cubic units.

Or as a formula:

\(V=abc\)

where \(a\), \(b\) and \(c\) are the lengths shown in the diagram.

Worked Example

The diagram shows a truck.

Find the volume of the load-carrying part of the truck.

Volume of Cylinders

The volume of a cylinder is given by the area of the circular base multiplied by its length (or height.)

Or as a formula:

The volume of a cylinder is given by

\(V=\pi r^{2} h\)

where \(r\) is the radius of the cylinder and \(h\) is its height.

Worked Example

The cylindrical body of a fire extinguisher has the dimensions shown in the diagram.

Find the maximum volume of water the extinguisher could hold.

Volume of Triangular Prisms

The volume of tiangular prism is given by the area of the triangular base multiplied by its length(or height)

Or as a formula:

The volume of a triangular prism is given by

\(V=A\;l\)

where \(A\) is the area of the end and \(l\) the length of the prism

or

\(V=\frac {1}{2} bhl\)

where \(b\) is the base of the triangle, \(h\) is the height of the triangle and \(l\) is the length of the prism.

Worked Example

A traffic calming road hump (sleeping policeman) is made of concrete and has the dimensions shown in the diagram.

Find the volume of concrete needed to make one road hump.

Volume

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