Final answer:
The total volume of a pool with square cross-sections perpendicular to the ground is found by multiplying the area of the square with the length of the pool. If the cross-sectional area does not change along the length, calculation is straightforward, otherwise, integration is needed.
Step-by-step explanation:
To find the total volume of a pool with a given condition for the cross-sections, one can use the concept that the volume (V) of a three-dimensional object with parallel sides is the cross-sectional area (A) multiplied by the height (h), as expressed in the equation V = Ah.
This concept is particularly useful when dealing with shapes like cylinders, where the volume is computed as the area of the base times the height. To visualize the volume of the pool with square cross-sections, imagine slicing the pool into a series of square sections along its length.
If these cross sections are perpendicular to the ground and parallel to the y-axis, as stated, each section would have an area of 'a squared' (a²) if 'a' represents the side of the square. Applying the formula for volume, one would multiply the area of one square by the length of the pool to find the total volume.
Concretely, if the pool has a constant square cross-sectional area along its length, the volume is straightforward to calculate. However, if the cross-sectional area changes, one would typically integrate the varying area along the length of the pool to find the total volume.
In this case, further information is required about how the dimensions of the cross-sectional area change with respect to the length of the pool. Without such information, the total volume cannot be precisely calculated.