An engineer decides to use a successful dam design for a new lake of the same depth. If the new lake has ten times the surface area as the lake held by the original dam, what, if any, design changes are necessary for the new dam to hold back the increased amount of water? Explain your reasoning.

Why would surface area have anything to do with it?

In order to determine the design changes necessary for the new dam to hold back the increased amount of water, we need to understand the relationship between the surface area of the lake and the capacity of the dam.

The capacity of a dam is determined by its height, width, and the strength of its materials. The surface area of the lake, on the other hand, is determined by the length and width of the lake.

Given that the new lake has ten times the surface area as the lake held by the original dam, we can assume that the length and width of the new lake are also ten times greater.

Since the depth of the lake remains the same, and the length and width are scaled up by a factor of ten, it means that the volume of water in the new lake is also ten times larger than the original lake.

To hold back the increased amount of water, the new dam would need to have a larger capacity compared to the original dam. This can be achieved by increasing the height, width, or using stronger materials for construction.

However, it's important to note that calculating the exact design changes required would require detailed engineering analysis, taking into consideration various factors such as the type of soil, hydrological conditions, and safety factors.

In summary, to hold back the increased amount of water in the new lake, the engineer would need to make design changes to increase the capacity of the new dam, such as increasing its height, width, or using stronger materials.