Final Answer:
The estimated volume of water in the swimming pool is approximately 576 cubic meters.
Step-by-step explanation:
To estimate the volume of the swimming pool, the recorded depths at 2-meter intervals need to be used to approximate the pool's shape. The pool is 8 meters by 12 meters, and the depths are measured at regular 2-meter intervals. This data gives an insight into how the depth varies across the pool.
Using this data, an estimation of the pool's shape can be visualized. The shape is likely a rectangular prism, with the depth values providing an idea of the changes in height at different sections of the pool. By dividing the pool into intervals and considering each section as a rectangular prism, an approximation of the volume for each section can be calculated using the dimensions provided (8m by 12m by varying depths).
To estimate the volume, the average depth in each 2-meter interval can be taken and multiplied by the area of the pool (8m by 12m). This provides an estimate of the volume of water in each section. Then, by summing up these estimated volumes for all intervals, the approximate total volume of water in the pool can be obtained.
Remember, this is an approximation. The accuracy of the estimated volume depends on the assumption that the pool's shape between measured points is consistent and doesn't vary significantly, which might not always be the case due to irregularities or curves in the pool's base or walls. However, this method gives a reasonable estimate based on the provided interval data.