Let the growth of the tumor in body. In early stages growth rate is limited by amount of nutrients (e.g. oxygen) which can be absorbed through surface. This has to be utilized for growth over full volume, V (t). In this phase, tumors are hardly dangerous. Later, using the process called as chemotaxis (tumor releases the chemical which \lures" blood vessels toward it), blood vessels may attach to tumor, permitting the almost unlimited supply of nutrients.
Suppose tumor to be spherical, write the differential equation for growth rate of radius, r(t), of tumor if it is in first (avascular) phase and rate of change of volume is proportional to surface area divided by volume with constant of proportionality k1. Solve equation if initial radius r(0) = 1 mm. Note volume of the sphere of radius r is V = 4 3r3 and surface area is S = 4r2.