Surface area and volume of regular composite solids

A major part in Further Mathematics is determining different physical characteristics of various shapes and sizes. This is an important skill needed for all questions throughout the exam as the application of maths starts with basic surface area calculations or volume calculations.

Regular Shapes

Some of the following formulae are provided by VCAA during the examination but being already familiarised with each shape and formula saves vital time during the exam.

Surface area Formulae


Surface area of Sphere 4πr²

Volume Formulae

Volume of Sphere 4/3πr²
Volume of Cone 1/3πr²h
Volume of Cylinder πr²h
Volume of Prism Base area x Height
Volume of Pyramid 1/3 x Base area x Height

Composite Shapes

Sometimes a combination of formulas and techniques are required to determine the volume or surface area of complex shapes.


Find the volume of the following shape. The radius is 5mm.

composite shape

The shape is made from a hemisphere and cylinder, hence there are two parts of the solution

total volume = volume of the hemisphere + volume of the cylinder
total volume = \frac{1}{2}*\frac{4}{3}\pi*5^3 + \pi * 5^2 * 7
total volume = 296.94 mm^3

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