Log-log plots of 18F-FDG uptake (TLA) versus metabolic tumour volume on diagnostic PET for breast cancer, head & neck cancer, non-small-cell lung cancer and rectal cancer display superlinear (β > 1) allometric scaling laws. Diagnostic PET with proliferation radiotracers, either 18F-FLT for breast cancer or 18F-FCHOL for glioma, shows the same dependence pointing to the use of glucose mostly as a resource for biosynthesis. The fitted exponents cluster around β = 5/4. Joint records of patients imaged in the same institution with identical protocol (breast-FDG, lung and rectal cancers), show that a common scaling law governs the dynamics. Error bars in (g) correspond to the standard error in the fitted parameter β obtained using fitlm.