1. **Problem statement:** An aquarium 5 ft long, 3 ft wide, and 2 ft deep is full of water with weight density 62.5 lb/ft³. (a) Find the hydrostatic pressure on the bottom. (b) Find the hydrostatic force on the bottom. (c) Find the hydrostatic force on one end. --- 2. **Formulas and rules:** - Hydrostatic pressure at depth $h$ is given by $P = \rho g h$, where $\rho g$ is the weight density. - Hydrostatic force on a surface is pressure times area: $F = P \times A$. - Pressure varies with depth, but on the bottom, depth is constant. --- 3. **(a) Hydrostatic pressure on the bottom:** - Depth $h = 2$ ft - Weight density $\rho g = 62.5$ lb/ft³ $$P = 62.5 \times 2 = 125 \text{ lb/ft}^2$$ --- 4. **(b) Hydrostatic force on the bottom:** - Area of bottom $A = 5 \times 3 = 15$ ft² - Force $F = P \times A = 125 \times 15 = 1875$ lb --- 5. **(c) Hydrostatic force on one end:** - One end is a rectangle 3 ft wide and 2 ft deep. - Pressure varies linearly from 0 at surface to $P=125$ lb/ft² at bottom. - Average pressure on end is $\frac{0 + 125}{2} = 62.5$ lb/ft² - Area $A = 3 \times 2 = 6$ ft² $$F = 62.5 \times 6 = 375 \text{ lb}$$ --- **Final answers:** (a) $125$ lb/ft² (b) $1875$ lb (c) $375$ lb