Potholes are very important factors to be considered in taking decisions on road repairs and management. Roads that require little maintenance to bring it back to its normal shape are left unattended to because of inadequate knowledge of their surface area and volume. Therefore stakeholders on road, particularly Government and site engineers, are always concerned with the surface area and volume of these potholes so that they can determine the amount of materials to be used for the repair and the amount of money to budget for it. Scientific estimation of the surface area and volume of potholes on a given length of road is a major problem to stakeholders. This paper therefore presents the use of surface and volume integrals, coupled with the idea of mathematical expectation, in finding the surface area and volume of potholes on a given length of road. We assumed that all the potholes have the same shape of circular paraboloid and considered some case studies to illustrate the significance of the model. The model is found to be appropriate for stakeholders on road to determine the amount of materials and money to budget for road repairs.