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Early calculations of area and volume are explained. It is shown that in ancient Egypt, use of regular shapes was needed to divide up land following annual flooding from the Nile. It is explained that the same principle of using regular shapes helped calculate volumes, for example to work out amounts of building materials needed for different structures. The importance of the ancient Greeks in making major advances in geometric calculations is shown through a bank-heist style sketch featuring Archimedes. A basic version of the method of exhaustion is shown as a way of calculating the area of a circle by subscribing it with many-sided polygons. As a further step, it is shown that the volume of a sphere can be calculated by dividing the sphere into a series of slim cylinders, the volumes of which can then be added together. The equation for the volume of a sphere based on pi is introduced by the Chinese mathematician Zu Gengzhi.

Explore the maths relating to specific shapes in more detail, for example breaking apart a triangle to form a rectangle, to help explain why its area is half times base times height. Use the example of Archimedes and the method of exhaustion as a way of explaining that pi is nothing more than a particular ratio. Discuss the idea that volume of a sphere can be approximated by adding the volumes of slim cylinders together.