In vitro tumour spheroid experiments have been used to study avascular tumour growth and drug design for the last 50 years. Unlike simpler two-dimensional cell cultures, tumour spheroids exhibit heterogeneity within the growing population of cells that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing population, giving rise to the notion of a four-dimensional (4D) tumour spheroid. In this work we develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data qualitatively and quantitatively compare very well with experimental data from a suite of 4D tumour spheroid experiments performed with a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is very difficult to measure these data in standard tumour spheroid experiments. Software required to implement the IBM is available on GitHub.