Question: You are designing a concrete slab. The architectural plans (from the US) state the required floor area is $500 \text{ ft}^2$. However, your local supplier in the Philippines sells concrete strictly in cubic meters ($\text{m}^3$). If the slab needs to be 6 inches thick, how many cubic meters of concrete must you order? (Use $1 \text{ ft} = 0.3048 \text{ m}$ and $1 \text{ in} = 0.0254 \text{ m}$).

Question: You are calculating the total pressure ($P$) exerted by a column of water on a dam. The formula provided is $P = \rho \cdot g \cdot h$, where $\rho$ (density) is in $\text{kg/m}^3$, $g$ (gravity) is in $\text{m/s}^2$, and $h$ (height) is in meters ($\text{m}$). Prove through dimensional analysis that the resulting unit for Pressure is correctly the Pascal ($\text{Pa}$).

Question: A geotechnical report states the density of a local soil sample is $125 \text{ lb/ft}^3$. You need to input this value into a European structural design software that strictly accepts density in kilograms per cubic meter ($\text{kg/m}^3$). Convert the density. (Use $1 \text{ lb} = 0.453592 \text{ kg}$ and $1 \text{ ft} = 0.3048 \text{ m}$).

Question: A surveyor measures a rectangular plot of land. The length is measured with a high-precision laser to be $125.43 \text{ m}$. The width is measured with a standard surveyor's tape and is recorded as $45.2 \text{ m}$. Calculate the total area of the plot and express the answer with the correct number of significant figures.