Advanced Shapes and Theorems

Engineering case studies and examples focusing on earthworks and complex storage volumes.

Case Studies: Engineering Applications

Case Study 1: Earthworks Estimation

A contractor needs to excavate a perfectly cylindrical hole for a deep foundation pier. The specified diameter is 1.5 m1.5\text{ m} and the depth is 12 m12\text{ m}. Due to soil expansion upon excavation, the loose soil volume increases by 20%20\% compared to its in-ground state. The contractor uses dump trucks with a capacity of 10 m310\text{ m}^3. How many truckloads are required to remove all the excavated soil?

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Case Study 2: Storage Tank Capacity

An industrial chemical plant requires a new storage vessel. The design consists of a main cylindrical body with a hemispherical top and a flat circular bottom. The cylinder has a diameter of 4 m4\text{ m} and a height of 5 m5\text{ m}. What is the total maximum volume of liquid this composite tank can hold?

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