A cylindrical concrete sample has a radius of $7.5 \, \text{cm}$ and a height of $30.0 \, \text{cm}$. Its mass is measured to be $12.5 \, \text{kg}$. Calculate its density in $\text{g/cm}^3$.

An engineer needs to determine if a specific hydraulic oil will float on water. A $500 \, \text{mL}$ sample of the oil has a mass of $435 \, \text{g}$. Calculate the specific gravity of the oil and determine its buoyancy in water at $4^\circ\text{C}$ (density of water $= 1.00 \, \text{g/mL}$).

A new lightweight structural beam is designed using an alloy made of $70\%$ Aluminum (density $= 2.70 \, \text{g/cm}^3$) and $30\%$ Magnesium (density $= 1.74 \, \text{g/cm}^3$) by volume. Calculate the theoretical density of this new alloy.

An engineer measures three segments of a pipe. The lengths are $15.2 \, \text{m}$, $3.14 \, \text{m}$, and $0.852 \, \text{m}$. What is the total length of the pipe assembly, adhering to rules for significant figures?

A chemical storage tank holds $4500$ gallons of a solvent. Convert this volume to cubic meters ($\text{m}^3$), maintaining the correct number of significant figures. (Assume $1 \, \text{gallon} = 3.78541 \, \text{L}$, and $1000 \, \text{L} = 1 \, \text{m}^3$). The value "$4500$" is known to be exact to two significant figures.

You are calculating the pressure exerted by a block of steel on the ground. The block has dimensions $1.20 \, \text{m} \times 0.50 \, \text{m} \times 2.00 \, \text{m}$ and the density of the steel is $7850 \, \text{kg/m}^3$. Calculate the pressure $P$ in Pascals ($P = F/A$) exerted on the $1.20 \, \text{m} \times 0.50 \, \text{m}$ face. Use $g = 9.81 \, \text{m/s}^2$. Apply proper significant figures at the final step.

A civil engineer is ordering materials for a new site. They evaluate structural steel, pure copper wiring, Portland cement, and distilled water for mixing. Classify each of these materials as an element, compound, homogeneous mixture, or heterogeneous mixture.

During the construction of a reinforced concrete structure, several processes occur: A) Rebar is bent into shape. B) Steel exposed to moisture begins to rust. C) Water freezes in the pores of poorly cured concrete, causing spalling. D) Cement reacts with water to harden (hydration). Identify each process as a physical or chemical change.

An environmental engineer is designing a chemical treatment process for wastewater. $500 \, \text{kg}$ of contaminated water is treated with $25 \, \text{kg}$ of a precipitating agent. After the reaction, a solid sludge forms, and the clean water is separated. If $490 \, \text{kg}$ of clean water is recovered, and assuming a closed system with no evaporation, what must be the mass of the solid sludge?

A civil engineer is analyzing a small hydroelectric setup. Water falls from a reservoir $50 \, \text{meters}$ above a turbine. The water has high potential energy at the top, which converts to kinetic energy as it falls, and is then converted to electrical energy by the generator. If $1000 \, \text{kg}$ of water falls, what is its initial potential energy relative to the turbine? (Use $g = 9.81 \, \text{m/s}^2$).